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2. New Trends in Complex Analysis Research.
- Author
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Oros, Georgia Irina
- Subjects
ANALYTIC functions ,UNIVALENT functions ,TREND analysis ,GEOMETRIC function theory ,FUNCTIONS of several complex variables ,MEROMORPHIC functions ,SYMMETRIC functions - Abstract
This document is a summary of a special issue of the journal "Mathematics" that focuses on new trends in complex analysis research. The issue includes 14 papers that cover various aspects of complex-valued functions of one or several complex variables. The papers explore topics such as coefficient estimates, starlikeness and convexity of analytic functions, holomorphic and bi-univalent functions, and integral operators. The research presented in the papers aims to contribute to the development of complex analysis and inspire further studies in the field. The document also acknowledges the authors and reviewers who contributed to the special issue's success. [Extracted from the article]
- Published
- 2024
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3. New Developments in Geometric Function Theory II.
- Author
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Oros, Georgia Irina
- Subjects
GEOMETRIC function theory ,UNIVALENT functions ,ANALYTIC functions ,MEROMORPHIC functions ,SYMMETRIC functions ,HYPERGEOMETRIC functions ,INVERSE functions - Abstract
This document is a summary of a special issue of the journal Axioms titled "New Developments in Geometric Function Theory II." The special issue contains 14 research papers that explore various topics related to complex-valued functions in the field of Geometric Function Theory. The papers cover subjects such as coefficient estimates, subordination theories, hypergeometric functions, and differential operators. Each paper presents new findings and results that contribute to the development of Geometric Function Theory. The special issue is recommended for researchers and scholars interested in this field of study. The document also acknowledges the authors, reviewers, and editors involved in the creation of the special issue. [Extracted from the article]
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- 2024
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4. Weighted Milne-type inequalities through Riemann-Liouville fractional integrals and diverse function classes.
- Author
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Almoneef, Areej A., Hyder, Abd-Allah, and Budak, Hüseyin
- Subjects
FRACTIONAL integrals ,INTEGRAL functions ,FUNCTIONS of bounded variation ,CONVEX functions ,DIFFERENTIABLE functions ,ANALYTIC functions - Abstract
This research paper investigated weighted Milne-type inequalities utilizing Riemann-Liouville fractional integrals across diverse function classes. A key contribution lies in the establishment of a fundamental integral equality, facilitated by the use of a nonnegative weighted function, which is pivotal for deriving the main results. The paper systematically proved weighted Milne-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. The obtained results not only contribute to the understanding of Milne-type inequalities but also offer insights that pave the way for potential future research in the considered topics. Furthermore, it is evident that the results obtained encompass numerous findings that were previously presented in various studies as special cases. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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5. A Composition Formula for the Modified Analytic Function Space Fourier–Feynman Transform.
- Author
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Chung, Hyun Soo
- Subjects
WIENER processes ,FUNCTION spaces ,ANALYTIC spaces ,ANALYTIC functions ,GAUSSIAN processes - Abstract
Composition formula is one of the most important research topics in functional analysis theory. Various relationships can be obtained using the composition formula. Since the generalized Brownian motion process used in this paper has a non-zero mean function, there are many restrictions on obtaining a composition formula for the modified analytic function space Fourier–Feynman transform. This paper contains an idea of how the composition Formula (9) below is established for the modified analytic function space Fourier–Feynman transform on function space. Using this idea, we are able to solve a problem that had never been solved before. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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6. The Mean Square of the Hurwitz Zeta-Function in Short Intervals.
- Author
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Laurinčikas, Antanas and Šiaučiūnas, Darius
- Subjects
ALGEBRAIC number theory ,SYSTEMS theory ,PRIME numbers ,ANALYTIC functions ,ARITHMETIC series ,ZETA functions - Abstract
The Hurwitz zeta-function ζ (s , α) , s = σ + i t , with parameter 0 < α ⩽ 1 is a generalization of the Riemann zeta-function ζ (s) ( ζ (s , 1) = ζ (s) ) and was introduced at the end of the 19th century. The function ζ (s , α) plays an important role in investigations of the distribution of prime numbers in arithmetic progression and has applications in special function theory, algebraic number theory, dynamical system theory, other fields of mathematics, and even physics. The function ζ (s , α) is the main example of zeta-functions without Euler's product (except for the cases α = 1 , α = 1 / 2 ), and its value distribution is governed by arithmetical properties of α. For the majority of zeta-functions, ζ (s , α) for some α is universal, i.e., its shifts ζ (s + i τ , α) , τ ∈ R , approximate every analytic function defined in the strip { s : 1 / 2 < σ < 1 } . For needs of effectivization of the universality property for ζ (s , α) , the interval for τ must be as short as possible, and this can be achieved by using the mean square estimate for ζ (σ + i t , α) in short intervals. In this paper, we obtain the bound O (H) for that mean square over the interval [ T − H , T + H ] , with T 27 / 82 ⩽ H ⩽ T σ and 1 / 2 < σ ⩽ 7 / 12 . This is the first result on the mean square for ζ (s , α) in short intervals. In forthcoming papers, this estimate will be applied for proof of universality for ζ (s , α) and other zeta-functions in short intervals. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Fractional Calculus and Hypergeometric Functions in Complex Analysis.
- Author
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Oros, Gheorghe and Oros, Georgia Irina
- Subjects
FRACTIONAL calculus ,HYPERGEOMETRIC functions ,ANALYTIC functions ,GEOMETRIC function theory ,HANKEL functions ,MEROMORPHIC functions ,SPECIAL functions - Abstract
This document titled "Fractional Calculus and Hypergeometric Functions in Complex Analysis" explores the impact of fractional calculus on various scientific and engineering disciplines. It emphasizes the significance of fractional operators in the study of fractional calculus and their applications in complex analysis research, specifically in the theory of univalent functions. The document also introduces hypergeometric functions and their connection to the theory of univalent functions. It compiles 12 research papers that cover topics such as geometric properties of fractional differential operators, logarithmic-related problems of univalent functions, and the study of generalized bi-subordinate functions. This document serves as a valuable resource for researchers interested in these subjects and their applications in complex analysis. Additionally, it provides a summary of three articles published in the Special Issue on "Fractional Calculus and Hypergeometric Functions in Complex Analysis." The first article explores the use of the Sălăgean q-differential operator for meromorphic multivalent functions, introducing new subclasses of functions. The second article presents three general double-series identities using Whipple transformations for terminating generalized hypergeometric functions, which can be used to derive additional identities. The third article defines a new generalized domain based on the quotient of two analytic functions and investigates the upper bounds of certain coefficients and determinants. The authors anticipate that these findings will inspire further research in the field. [Extracted from the article]
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- 2024
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8. A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials
- Author
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Eie, Minking
- Published
- 1996
9. The Generalized Fox–Wright Function: The Laplace Transform, the Erdélyi–Kober Fractional Integral and Its Role in Fractional Calculus.
- Author
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Paneva-Konovska, Jordanka and Kiryakova, Virginia
- Subjects
FRACTIONAL integrals ,FRACTIONAL calculus ,MATHEMATICAL functions ,ANALYTIC functions ,INTEGRAL functions ,HYPERGEOMETRIC functions ,SPECIAL functions ,LAPLACE transformation - Abstract
In this paper, we consider and study in detail the generalized Fox–Wright function Ψ ˜ q p introduced in our recent work as an extension of the Fox–Wright function Ψ q p . This special function can be seen as an important case of the so-called I-functions of Rathie and H ¯ -functions of Inayat-Hussain, that in turn extend the Fox H-functions and appear to include some Feynman integrals in statistical physics, in polylogarithms, in Riemann Zeta-type functions and in other important mathematical functions. Depending on the parameters, Ψ ˜ q p is an entire function or is analytic in an open disc with a final radius. We derive its basic properties, such as its order and type, and its images under the Laplace transform and under classical fractional-order integrals. Particular cases of Ψ ˜ q p are specified, including the Mittag-Leffler and Le Roy-type functions and their multi-index analogues and many other special functions of Fractional Calculus. The corresponding results are illustrated. Finally, we emphasize the role of these new generalized hypergeometric functions as eigenfunctions of operators of new Fractional Calculus with specific I-functions as singular kernels. This paper can be considered as a natural supplement to our previous surveys "Going Next after 'A Guide to Special Functions in Fractional Calculus': A Discussion Survey", and "A Guide to Special Functions of Fractional Calculus", published recently in this journal. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. FURTHER DEVELOPMENT ON KRASNER-VUKOVIĆ PARAGRADED STRUCTURES AND p-ADIC INTERPOLATION OF YUBO JIN L-VALUES.
- Author
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PANCHISHKIN, ALEXEI
- Subjects
AUTOMORPHIC forms ,ANALYTIC functions ,DIFFERENTIAL operators ,UNITARY groups ,ALGEBRAIC numbers - Abstract
This paper is a joint project with Siegfried Bocherer (Mannheim), developing a recent preprint of Yubo Jin (Durham UK) previous works of Anh Tuan Do (Vietnam) and Dubrovnik, IUC-2016 papers from Sarajevo Journal of Mathematics (Vol.12, No.2-Suppl., 2016). We wish to use paragraded structures [KrVu87], [Vu01] on differential operators and arithmetical automorphic forms on classical groups and show that these structures provide a tool to construct p-adic measures and p-adic L-functions on the corresponding non-archimedean weight spaces. An approach to constructions of automorphic L-functions on unitary groups and their p-adic analogues is presented. For an algebraic group G over a number field K these L functions are certain Euler products L(s, π, r, χ). In particular, our constructions cover the L-functions in [Shi00] via the doubling method of Piatetski-Shapiro and Rallis. A p-adic analogue of L(s, π, r, χ) is a p-adic analytic function L
p (s, π, r, χ) of p-adic arguments s ∊ Zp , χ mod pr which interpolates algebraic numbers defined through the normalized critical values L*(s, π, r, χ) of the corresponding complex analytic L-function. We present a method using arithmetic nearlyholomorphic forms and general quasi-modular forms, related to algebraic automorphic forms. It gives a technique of constructing p-adic zeta-functions via general quasi-modular forms and their Fourier coefficients. [ABSTRACT FROM AUTHOR]- Published
- 2024
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11. On the Spectrum of the Non-Selfadjoint Differential Operator with an Integral Boundary Condition and NegativeWeight Function.
- Author
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Çoşkun, Nimet and Görgülü, Merve
- Subjects
DIFFERENTIAL operators ,GENERALIZATION ,HYPERBOLIC functions ,EIGENVALUES ,ANALYTIC functions - Abstract
In this paper, we shall study the spectral properties of the non-selfadjoint operator in the space ... generated by the Sturm-Liouville differential equation ... with the integral type boundary condition ... and the non-standard weight function ρ (x) = -1 where ... . There are an enormous number of papers considering the positive values of ρ (x) for both continuous and discontinuous cases. The structure of the weight function affects the analytical properties and representations of the solutions of the equation. Differently from the classical literature, we used the hyperbolic type representations of the fundamental solutions of the equation to obtain the spectrum of the operator. Moreover, the conditions for the finiteness of the eigenvalues and spectral singularities were presented. Hence, besides generalizing the recent results, Naimark's and Pavlov's conditions were adopted for the negative weight function case. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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12. Analytic Besov functional calculus for several commuting operators.
- Author
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Batty, Charles, Gomilko, Alexander, Kobos, Dominik, and Tomilov, Yuri
- Subjects
CALCULUS ,ANALYTIC functions ,BANACH spaces - Abstract
This paper investigates analytic Besov functions of n variables which act on the generators of n commuting C
0 -semigroups on a Banach space. The theory for n = 1 has already been published, and the present paper uses a different approach to that case as well as extending to the cases when n ≥ 2. It also clarifies some spectral mapping properties and provides some operator norm estimates. [ABSTRACT FROM AUTHOR]- Published
- 2024
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13. AN OPERATOR RICCATI EQUATION AND REFLECTIONLESS SCHR¨ODINGER OPERATORS.
- Author
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MYKYTYUK, YA. V. and SUSHCHYK, N. S.
- Subjects
RICCATI equation ,SCHRODINGER operator ,HILBERT space ,ANALYTIC functions ,OPERATOR-valued measures ,BANACH algebras ,LINEAR operators - Abstract
In this paper, we study a connection between the operator Riccati equation S′(x) = KS(x) + S(x)K - 2S(x)KS(x), x ∈ R, and the set of reflectionless Schr¨odinger operators with operator-valued potentials. Here K ∈ B(H), K > 0 and S: R → B(H), where B(H) is the Banach algebra of all linear continuous operators acting in a separable Hilbert space H. Let S+(K) be the set of all solutions S of the Riccati equation satisfying the conditions 0 < S(0) < I and S′(0) ≥ 0, with I being the identity operator in H. We show that every solution S ∈ S+(K) generates a reflectionless Schr¨odinger operator with some potential q that is an analytic function in the strip... [ABSTRACT FROM AUTHOR]
- Published
- 2024
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14. Bi-Concave Functions Connected with the Combination of the Binomial Series and the Confluent Hypergeometric Function.
- Author
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Srivastava, Hari M., El-Deeb, Sheza M., Breaz, Daniel, Cotîrlă, Luminita-Ioana, and Sălăgean, Grigore Stefan
- Subjects
HYPERGEOMETRIC functions ,HYPERGEOMETRIC series ,UNIVALENT functions ,ANALYTIC functions ,GAUSSIAN function - Abstract
In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confluent hypergeometric function. Among some other properties and results, we derive the estimates on the initial Taylor-Maclaurin coefficients | a 2 | and | a 3 | for functions in these analytic and bi-concave function classes, which are introduced in this paper. We also derive a number of corollaries and consequences of our main results in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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15. Certified numerical real root isolation for bivariate nonlinear systems.
- Author
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Cheng, Jin-San, Wen, Junyi, and Zhang, Bingwei
- Subjects
- *
NUMERICAL roots , *NONLINEAR systems , *BIVARIATE analysis , *CONFERENCE papers , *ANALYTIC functions - Abstract
In this paper, we present a new method for isolating real roots of a bivariate nonlinear system. It is a subdivision method based on analyzing the local geometrical properties of the given system. We propose the concept of opposite monotone system in a box and use it to determine the existence and the uniqueness of a simple real zero of the system in the box. We have implemented our method and the experiments show the effectivity and efficiency of our approach, especially for high degree sparse polynomial systems. This paper is an extended version of the ISSAC'19 conference paper (Cheng and Wen (2019)). [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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16. New Developments in Geometric Function Theory.
- Author
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Oros, Georgia Irina
- Subjects
GEOMETRIC function theory ,UNIVALENT functions ,ANALYTIC functions ,MEROMORPHIC functions ,CONVEX functions ,FRACTIONAL calculus - Abstract
A previously introduced operator defined by applying the Riemann-Liouville fractional integral to the convex combination of well-known Ruscheweyh and Salagean differential operators is used for defining a new fuzzy subclass. The authors suggest that the operator introduced here can be utilized to define other classes of analytic functions or to generalize other types of differential operators. The new operator defined in this paper can be used to introduce other specific subclasses of analytic functions, and quantum calculus can be also investigated in future studies. The fractional differential operator and the Mittag-Leffler functions are combined to formulate and arrange a new operator of fractional calculus. [Extracted from the article]
- Published
- 2023
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17. Differentiation Formulas for Analytic Functions
- Author
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Lyness, J. N.
- Published
- 1968
- Full Text
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18. Chebyshev's Method for Multiple Zeros of Analytic Functions: Convergence, Dynamics and Real-World Applications.
- Author
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Kostadinova, Stoyanka G. and Ivanov, Stoil I.
- Subjects
ANALYTIC functions - Abstract
This paper deals with the convergence and dynamics of Chebyshev's method for simple and multiple zeros of analytic functions. We establish a local convergence theorem that provides error estimates and exact domains of initial approximations to guarantee the Q-cubic convergence of the method right from the first iteration. Applications to some real-world problems as well as theoretical and numerical comparison with the famous Halley's method are also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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19. Differential Subordination and Coefficient Functionals of Univalent Functions Related to cos z.
- Author
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Rai, P. and Kumar, S.
- Subjects
TRIGONOMETRIC functions ,STAR-like functions ,ANALYTIC functions ,CONVEX functions ,FUNCTIONALS ,UNIVALENT functions ,HYPERGEOMETRIC functions - Abstract
Differential subordination in the complex plane is the generalization of a differential inequality on the real line. In this paper, we consider two subclasses of univalent functions associated with the trigonometric function cos z. Using some properties of the hypergeometric functions, we determine the sharp estimate on the parameter β such that the analytic function p(z) satisfying p(0) = 1, is subordinate to cos z when the differential expression p(z) + βz(dp(z)/dz) is subordinate to the Janowski function. We compute sharp bounds on coefficient functional Hermitian-Toeplitz determinants of the third and the fourth order with an invariance property for such functions. In addition, we estimate bound on Hankel determinants of the second and the third order. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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20. Sălăgean Differential Operator in Connection with Stirling Numbers.
- Author
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Frasin, Basem Aref and Cotîrlă, Luminiţa-Ioana
- Subjects
GEOMETRIC function theory ,NEGATIVE binomial distribution ,DIFFERENTIAL operators ,INTEGRAL operators ,ANALYTIC functions - Abstract
Sălăgean differential operator D κ plays an important role in the geometric function theory, where many studies are using this operator to introduce new subclasses of analytic functions defined in the open unit disk. Studies of Sălăgean differential operator D κ in connection with Stirling numbers are relatively new. In this paper, the differential operator D κ involving Stirling numbers is considered. A new sufficient condition involving Stirling numbers for the series Υ θ s (ϰ) written with the Pascal distribution are discussed for the subclass T κ (ϵ , ♭) . Also, we provide a sufficient condition for the inclusion relation I θ s R ϖ (E , D ) ⊂ T κ (ϵ , ♭) . Further, we consider the properties of an integral operator related to Pascal distribution series. New special cases as a consequences of the main results are also obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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21. Applications of Mittag–Leffler Functions on a Subclass of Meromorphic Functions Influenced by the Definition of a Non-Newtonian Derivative.
- Author
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Breaz, Daniel, Karthikeyan, Kadhavoor R., and Murugusundaramoorthy, Gangadharan
- Subjects
ANALYTIC functions ,SYMMETRIC functions ,UNIVALENT functions ,SCHWARZ function ,STAR-like functions ,MEROMORPHIC functions - Abstract
In this paper, we defined a new family of meromorphic functions whose analytic characterization was motivated by the definition of the multiplicative derivative. Replacing the ordinary derivative with a multiplicative derivative in the subclass of starlike meromorphic functions made the class redundant; thus, major deviation or adaptation was required in defining a class of meromorphic functions influenced by the multiplicative derivative. In addition, we redefined the subclass of meromorphic functions analogous to the class of the functions with respect to symmetric points. Initial coefficient estimates and Fekete–Szegö inequalities were obtained for the defined function classes. Some examples along with graphs have been used to establish the inclusion and closure properties. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. Starlike Functions in the Space of Meromorphic Harmonic Functions.
- Author
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Dziok, Jacek
- Subjects
GEOMETRIC function theory ,MEROMORPHIC functions ,ANALYTIC functions ,ANALYTIC spaces ,FUNCTION spaces - Abstract
The Geometric Theory of Analytic Functions was initially developed for the space of functions that are analytic in the unit disk. The convexity and starlikeness of functions are the first geometric ideas considered in this theory. We can notice a symmetry between the subjects considered in the space of analytic functions and those in the space of harmonic functions. In the presented paper, we consider the starlikeness of functions in the space of meromorphic harmonic functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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23. Subclasses of Bi-Univalent Functions Connected with Caputo-Type Fractional Derivatives Based upon Lucas Polynomial.
- Author
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Alsager, Kholood M., Murugusundaramoorthy, Gangadharan, Breaz, Daniel, and El-Deeb, Sheza M.
- Subjects
STAR-like functions ,ANALYTIC functions ,CONVEX functions ,POLYNOMIALS ,UNIVALENT functions - Abstract
In the current paper, we introduce new subclasses of analytic and bi-univalent functions involving Caputo-type fractional derivatives subordinating to the Lucas polynomial. Furthermore, we find non-sharp estimates on the first two Taylor–Maclaurin coefficients a 2 and a 3 for functions in these subclasses. Using the values of a 2 and a 3 , we determined Fekete–Szegő inequality for functions in these subclasses. Moreover, we pointed out some more subclasses by fixing the parameters involved in Lucas polynomial and stated the estimates and Fekete–Szegő inequality results without proof. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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24. Fuzzy differential subordination and superordination results for the Mittag-Leffler type Pascal distribution.
- Author
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Soren, Madan Mohan and Cotîrla, Luminiţa-Ioana
- Subjects
NEGATIVE binomial distribution ,ANALYTIC functions ,UNIVALENT functions ,STAR-like functions - Abstract
In this paper, we derive several fuzzy differential subordination and fuzzy differential superordination results for analytic functions M
s,γ ξ,β , which involve the extended Mittag-Leffler function and the Pascal distribution series. We also investigate and introduce a class MBF,s,γ ξ,β (ρ) of analytic and univalent functions in the open unit disc D by employing the newly defined operator Ms,γ ξ,β . We determine a specific relationship of inclusion for this class. Further, we establish prerequisites for a function role in serving as both the fuzzy dominant and fuzzy subordinant of the fuzzy differential subordination and superordination, respectively. Some novel results that are sandwich-type can be found here. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
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25. A Linear Composition Operator on the Bloch Space.
- Author
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Zhu, Xiangling and Hu, Qinghua
- Subjects
ANALYTIC functions ,FUNCTION spaces ,ANALYTIC spaces ,LINEAR operators ,COMPOSITION operators - Abstract
Let n ∈ N 0 , ψ be an analytic self-map on D and u be an analytic function on D. The single operator D u , ψ n acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as (D u , ψ n f) (z) = u (z) f (n) (ψ (z)) , f ∈ H (D) . However, the study of the operator P u → , ψ k , which represents a finite sum of these operators with varying orders, remains incomplete. The boundedness, compactness and essential norm of the operator P u → , ψ k on the Bloch space are investigated in this paper, and several characterizations for these properties are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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26. Toeplitz Matrices for a Class of Bazilevič Functions and the λ -Pseudo-Starlike Functions.
- Author
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Wanas, Abbas Kareem, Sehen, Salam Abdulhussein, and Páll-Szabó, Ágnes Orsolya
- Subjects
TOEPLITZ matrices ,UNIVALENT functions ,MATRIX functions ,SYMMETRIC matrices ,FAMILIES - Abstract
In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the λ -pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices T 2 (2) , T 2 (3) , T 3 (1) and T 3 (2) for the functions in this family. Further, we investigate several special cases and consequences of our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. On the Fekete–Szegö Problem for Certain Classes of (γ , δ)-Starlike and (γ , δ)-Convex Functions Related to Quasi-Subordinations.
- Author
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Almutairi, Norah Saud, Shahen, Awatef, Cătaş, Adriana, and Darwish, Hanan
- Subjects
UNIVALENT functions ,ANALYTIC functions ,STAR-like functions - Abstract
In the present paper, we propose new generalized classes of (p,q)-starlike and (p,q)-convex functions. These classes are introduced by making use of a (p,q)-derivative operator. There are established Fekete–Szegö estimates | a 3 − μ a 2 2 | for functions belonging to the newly introduced subclasses. Certain subclasses of analytic univalent functions associated with quasi-subordination are defined. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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28. A General and Comprehensive Subclass of Univalent Functions Associated with Certain Geometric Functions.
- Author
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Al-Hawary, Tariq, Frasin, Basem, and Aldawish, Ibtisam
- Subjects
ANALYTIC functions ,HYPERGEOMETRIC functions ,SPECIAL functions ,BESSEL functions ,POISSON distribution - Abstract
In this paper, taking into account the intriguing recent results of Rabotnov functions, Poisson functions, Bessel functions and Wright functions, we consider a new comprehensive subclass O μ (Δ 1 , Δ 2 , Δ 3 , Δ 4) of univalent functions defined in the unit disk Λ = { τ ∈ C : τ < 1 } . More specifically, we investigate some sufficient conditions for Rabotnov functions, Poisson functions, Bessel functions and Wright functions to be in this subclass. Some corollaries of our main results are given. The novelty and the advantage of this research could inspire researchers of further studies to find new sufficient conditions to be in the subclass O μ (Δ 1 , Δ 2 , Δ 3 , Δ 4) not only for the aforementioned special functions but for different types of special functions, especially for hypergeometric functions, Dini functions, Sturve functions and others. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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29. Multidimensional Diffusion-Wave-Type Solutions to the Second-Order Evolutionary Equation.
- Author
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Kazakov, Alexander and Lempert, Anna
- Subjects
EVOLUTION equations ,ORDINARY differential equations ,DIFFERENTIAL equations ,PARTIAL differential equations ,MATHEMATICAL physics ,ANALYTIC functions - Abstract
The paper concerns a nonlinear second-order parabolic evolution equation, one of the well-known objects of mathematical physics, which describes the processes of high-temperature thermal conductivity, nonlinear diffusion, filtration of liquid in a porous medium and some other processes in continuum mechanics. A particular case of it is the well-known porous medium equation. Unlike previous studies, we consider the case of several spatial variables. We construct and study solutions that describe disturbances propagating over a zero background with a finite speed, usually called 'diffusion-wave-type solutions'. Such effects are atypical for parabolic equations and appear since the equation degenerates on manifolds where the desired function vanishes. The paper pays special attention to exact solutions of the required type, which can be expressed as either explicit or implicit formulas, as well as a reduction of the partial differential equation to an ordinary differential equation that cannot be integrated in quadratures. In this connection, Cauchy problems for second-order ordinary differential equations arise, inheriting the singularities of the original formulation. We prove the existence of continuously differentiable solutions for them. A new example, an analog of the classic example by S.V. Kovalevskaya for the considered case, is constructed. We also proved a new existence and uniqueness theorem of heat-wave-type solutions in the class of piece-wise analytic functions, generalizing previous ones. During the proof, we transit to the hodograph plane, which allows us to overcome the analytical difficulties. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Subordinations Results on a q -Derivative Differential Operator.
- Author
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Andrei, Loriana and Caus, Vasile-Aurel
- Subjects
DIFFERENTIAL operators ,ANALYTIC functions ,UNIVALENT functions ,INTEGRAL operators ,SET functions - Abstract
In this research paper, we utilize the q-derivative concept to formulate specific differential and integral operators denoted as R q n , m , λ , F q n , m , λ and G q n , m , λ . These operators are introduced with the aim of generalizing the class of Ruscheweyh operators within the set of univalent functions. We extract certain properties and characteristics of the set of differential subordinations employing specific techniques. By utilizing the newly defined operators, this paper goes on to establish subclasses of analytic functions defined on an open unit disc. Additionally, we delve into the convexity properties of the two recently introduced q-integral operators, F q n , m , λ and G q n , m , λ . Special cases of the primary findings are also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. On the analytic extension of the Horn’s hypergeometric function H4.
- Author
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R., Dmytryshyn, I.-A., Lutsiv, and M., Dmytryshyn
- Subjects
HYPERGEOMETRIC functions ,ANALYTIC functions ,CONTINUED fractions - Abstract
The paper establishes new convergence domains of branched continued fraction expansions of Horn’s hypergeometric function H
4 with real and complex parameters. These domains enabled the PC method to establish the analytical extension of analytical functions to their expansions in the studied domains of convergence. A few examples are provided at the end to illustrate this. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
32. Certain Quantum Operator Related to Generalized Mittag–Leffler Function.
- Author
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Yassen, Mansour F. and Attiya, Adel A.
- Subjects
QUANTUM operators ,GEOMETRIC function theory ,ANALYTIC functions ,OPERATOR functions ,DIFFERENTIAL operators - Abstract
In this paper, we present a novel class of analytic functions in the form h (z) = z p + ∑ k = p + 1 ∞ a k z k in the unit disk. These functions establish a connection between the extended Mittag–Leffler function and the quantum operator presented in this paper, which is denoted by ℵ q , p n (L , a , b) and is also an extension of the Raina function that combines with the Jackson derivative. Through the application of differential subordination methods, essential properties like bounds of coefficients and the Fekete–Szegő problem for this class are derived. Additionally, some results of special cases to this study that were previously studied were also highlighted. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
33. New definitions of fractional derivatives and integrals for complex analytic functions.
- Author
-
Abu-Ghuwaleh, Mohammad and Saadeh, Rania
- Subjects
FRACTIONAL calculus ,ANALYTIC functions ,MATHEMATICAL functions ,CAPUTO fractional derivatives ,SPECIAL functions ,ZETA functions ,DEFINITIONS - Abstract
In this paper, we introduce a ground-breaking approach to defining fractional calculus for a selected class of analytic functions. Our new definitions, based on a novel and intuitive understanding of fractional derivatives and integrals, offer improved mathematical tractability for a variety of applications, including physics, engineering and finance. Our approach significantly simplifies the complexity of mathematical functions compared to the traditional Riemann-Liouville approach, by using simple functions rather than special functions, while preserving the intrinsic sense of fractional calculus. This article not only presents our proposed definitions but also provides a thorough analysis of their properties and advantages. The conclusion of this paper discusses the potential for future research in the field of fractional calculus. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Coefficient Bounds for Some Families of Bi-Univalent Functions with Missing Coefficients †.
- Author
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Analouei Adegani, Ebrahim, Jafari, Mostafa, Bulboacă, Teodor, and Zaprawa, Paweł
- Subjects
GEOMETRIC function theory ,UNIVALENT functions ,COEFFICIENTS (Statistics) ,ANALYTIC functions ,TWENTIETH century - Abstract
A branch of complex analysis with a rich history is geometric function theory, which first appeared in the early 20th century. The function theory deals with a variety of analytical tools to study the geometric features of complex-valued functions. The main purpose of this paper is to estimate more accurate bounds for the coefficient | a n | of the functions that belong to a class of bi-univalent functions with missing coefficients that are defined by using the subordination. The significance of our present results consists of improvements to some previous results concerning different recent subclasses of bi-univalent functions, and the aim of this paper is to improve the results of previous outcomes. In addition, important examples of some classes of such functions are provided, which can help to understand the issues related to these functions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values.
- Author
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Carmichael, Richard D.
- Subjects
ANALYTIC functions ,HARDY spaces - Abstract
Vector-valued analytic functions in C n , which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space H p , 1 ≤ p < 2 , if the boundary value is in the vector-valued L p , 1 ≤ p < 2 , functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2 ≤ p ≤ ∞ . Thus, with the addition of the results of this paper, the considered problems are proved for all p , 1 ≤ p ≤ ∞ . [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Univalence criteria for analytic functions obtained using fuzzy differential subordinations.
- Author
-
OROS, Georgia Irina
- Subjects
GEOMETRIC function theory ,ANALYTIC functions ,FUZZY sets ,SET theory ,MATHEMATICIANS ,STAR-like functions ,UNIVALENT functions - Abstract
Ever since Lotfi A. Zadeh published the paper "Fuzzy Sets" in 1965 setting the basis of a new theory named fuzzy sets theory, many scientists have developed this theory and its applications. Mathematicians were especially interested in extending classical mathematical results in the fuzzy context. Such an extension was also done relating fuzzy sets theory and geometric theory of analytic functions. The study begun in 2011 has many interesting published outcomes and the present paper follows the line of the previous research in the field. The aim of the paper is to give some references related to the connections already made between fuzzy sets theory and geometric theory of analytic functions and to present some new results that might prove interesting for mathematicians willing to enlarge their views on certain aspects of the merge between the two theories. Using the notions of fuzzy differential subordination and the classical notion of differential subordination for analytic functions, two criteria for the univalence of the analytic functions are stated in this work. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
37. TOEPLITZ AND HANKEL OPERATORS AND DIXMIER TRACES ON THE UNIT BALL OF ℂⁿ
- Author
-
ENGLIŠ, MIROSLAV, GUO, KUNYU, and ZHANG, GENKAI
- Published
- 2009
- Full Text
- View/download PDF
38. Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators.
- Author
-
Ali, Ekram E., Vivas-Cortez, Miguel, and El-Ashwah, Rabha M.
- Subjects
GEOMETRIC function theory ,ANALYTIC functions ,SET theory ,FUZZY sets ,CHARACTERISTIC functions - Abstract
This paper's findings are related to geometric function theory (GFT). We employ one of the most recent methods in this area, the fuzzy admissible functions methodology, which is based on fuzzy differential subordination, to produce them. To do this, the relevant fuzzy admissible function classes must first be defined. This work deals with fuzzy differential subordinations, ideas borrowed from fuzzy set theory and applied to complex analysis. This work examines the characteristics of analytic functions and presents a class of operators in the open unit disk J η , ς κ (a , e , x) for ς > − 1 , η > 0 , such that a , e ∈ R , (e − a) ≥ 0 , a > − x . The fuzzy differential subordination results are obtained using (GFT) concepts outside the field of complex analysis because of the operator's compositional structure, and some relevant classes of admissible functions are studied by utilizing fuzzy differential subordination. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Certain Geometric Study Involving the Barnes–Mittag-Leffler Function.
- Author
-
Alenazi, Abdulaziz and Mehrez, Khaled
- Subjects
GAMMA functions ,STAR-like functions ,UNIVALENT functions ,CONVEX functions ,ANALYTIC functions - Abstract
The main purpose of this paper is to study certain geometric properties of a class of analytic functions involving the Barnes–Mittag-Leffler function. The main mathematical tools are the monotonicity patterns of some class of functions associated with the gamma and digamma functions. Furthermore, some consequences and examples are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. SOME PROPERTIES OF ANALYTIC FUNCTIONS DEFINED BY POLYLOGARITHM FUNCTIONS.
- Author
-
REDDY, P. THIRUPATHI
- Subjects
INTEGRAL operators ,UNIVALENT functions ,ANALYTIC functions - Abstract
The main purpose of this paper, is to introduce a new subclass of analytic functions involving Polylogarithm functions and obtain coefficient inequalities, distortion properties, extreme points, radii of starlikeness and convexity, Hadamard product, and convolution and integral operators for the class. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Approximation of the Hilbert Transform in Hölder Spaces.
- Author
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Aliev, R. A. and Alizade, L. Sh.
- Subjects
SINGULAR integrals ,ANALYTIC functions ,SYSTEMS theory ,FOURIER transforms ,NUMERICAL integration ,HILBERT transform - Abstract
The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. It is also the main part of the theory of singular integral equations on the real line. Therefore, approximations of Hilbert transform are of great interest. Many papers have dealt with the numerical approximation of singular integrals in case of bounded intervals. On the other hand, the literature concerning the numerical integration on unbounded intervals is much sparser than the one on bounded intervals. There is very little literature concerning the case of Hilbert transform. This article is dedicated to the approximation of Hilbert transform in Hölder spaces by the operators introduced by V.R.Kress and E.Mortensen to approximate the Hilbert transform of analytic functions in a strip. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Fekete-Szego results for certain BI-univalent functions involving q-analogues of logarithmic functions.
- Author
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Amini, Ebrahim, Al-Omari, Shrideh, and Al-Omari, Jafar
- Subjects
GEOMETRIC function theory ,DIFFERENTIAL operators ,LOGARITHMIC functions ,ANALYTIC functions ,OPERATOR functions - Abstract
In this paper, we discuss a novel type of analytic bi-univalent functions by utilizing specialized q-Salagean differential operators. Then, we use the q-analogue of the logarithmic function to introduce definition and provide properties of a class of bi-univalent functions. Further, we use the subordination principle to estimate the initial Taylor and Maclaurin coefficients for these given univalent functions. Additionally, we introduce new operators to demonstrate practical applications of the existing theory and establish Fakte-Szego results for each function in the defined sets. Further, we discuss certain coefficient inequalities in detail. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials.
- Author
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Hussen, Abdulmtalb, Madi, Mohammed S. A., and Abominjil, Abobaker M. M.
- Subjects
UNIVALENT functions ,POLYNOMIALS ,ANALYTIC functions - Abstract
In this paper, we introduced two novel subclasses of bi-univalent functions, M
Σ (α, B(x, ξ)) and HΣ (α, µ, B(x, ξ)), utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients |a2 | and |a3 |, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
44. Some Classes of Bazilevič-Type Close-to-Convex Functions Involving a New Derivative Operator.
- Author
-
Sabir, Pishtiwan Othman, Lupas, Alina Alb, Khalil, Sipal Saeed, Mohammed, Pshtiwan Othman, and Abdelwahed, Mohamed
- Subjects
STAR-like functions ,ANALYTIC functions ,UNIVALENT functions - Abstract
In the present paper, we are merging two interesting and well-known classes, namely those of Bazilevič and close-to-convex functions associated with a new derivative operator. We derive coefficient estimates for this broad category of analytic, univalent and bi-univalent functions and draw attention to the Fekete–Szegö inequalities relevant to functions defined within the open unit disk. Additionally, we identify several specific special cases of our results by specializing the parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Fourth order Hankel determinants for certain subclasses of modified sigmoid-activated analytic functions involving the trigonometric sine function.
- Author
-
Srivastava, Hari M., Khan, Nazar, Bah, Muhtarr A., Alahmade, Ayman, Tawfiq, Ferdous M. O., and Syed, Zainab
- Subjects
HANKEL functions ,SINE function ,ANALYTIC functions ,TRIGONOMETRIC functions ,UNIVALENT functions ,DIFFERENTIAL operators - Abstract
The aim of this paper is to introduce two new subclasses R sin m (ℑ) and R sin (ℑ) of analytic functions by making use of subordination involving the sine function and the modified sigmoid activation function ℑ (v) = 2 1 + e − v , v ≥ 0 in the open unit disc E. Our purpose is to obtain some initial coefficients, Fekete–Szego problems, and upper bounds for the third- and fourth-order Hankel determinants for the functions belonging to these two classes. All the bounds that we will find here are sharp. We also highlight some known consequences of our main results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Results for Analytic Function Associated with Briot–Bouquet Differential Subordinations and Linear Fractional Integral Operators.
- Author
-
Amini, Ebrahim, Salameh, Wael, Al-Omari, Shrideh, and Zureigat, Hamzeh
- Subjects
FRACTIONAL integrals ,DIFFERENTIAL operators ,HYPERGEOMETRIC functions ,GAUSSIAN function ,CONVEX sets ,INTEGRAL operators ,ANALYTIC functions - Abstract
In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. New Properties of Analytic Functions.
- Author
-
Güney, Hatun Özlem and Owa, Shigeyoshi
- Subjects
ANALYTIC functions ,STAR-like functions - Abstract
In the present paper, we consider the class A ¯ of functions f (z) of the form f (z) = z + ∑ k = 1 ∞ a 1 + k 3 z 1 + k 3 that are analytic in the open unit disc U. If a 1 + k 3 = 0 for k ≠ 3 n (n = 1 , 2 , 3 , ⋯) , then f (z) is given by f (z) = z + ∑ k = 2 ∞ a k z k. For such functions f (z) ∈ A ¯ , some interesting properties for subordinations and strongly starlike functions are given. Also, some interesting examples for the results are shown. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. Study of quantum calculus for a new subclass of q-starlike bi-univalent functions connected with vertical strip domain.
- Author
-
Abubaker, Ahmad A., Matarneh, Khaled, Khan, Mohammad Faisal, Al-Shaikh, Suha B., and Kamal, Mustafa
- Subjects
CALCULUS ,INVERSE functions ,ANALYTIC functions ,UNIVALENT functions ,STAR-like functions - Abstract
In this study, using the ideas of subordination and the quantum-difference operator, we established a new subclass S*(δ,σ, q) of q-starlike functions and the subclass S*σ (δ,σ, q) of q-starlike bi-univalent functions associated with the vertical strip domain. We examined sharp bounds for the first two Taylor-Maclaurin coefficients, sharp Fekete-Szegö type problems, and coefficient inequalities for the function h that belong to S*(δ,σ, q), as well as sharp bounds for the inverse function h that belong to S*(δ,σ, q). We also investigated some results for the class of bi-univalent functions S*σ (δ,σ, q) and well-known corollaries were also highlighted to show connections between previous results and the findings of this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations.
- Author
-
Sabir, Pishtiwan Othman
- Subjects
CONVEX functions ,UNIVALENT functions ,SYMMETRIC functions ,ANALYTIC functions ,SCHWARZ function ,STAR-like functions - Abstract
Starlike and convex functions have gained increased prominence in both academic literature and practical applications over the past decade. Concurrently, logarithmic coefficients play a pivotal role in estimating diverse properties within the realm of analytic functions, whether they are univalent or nonunivalent. In this paper, we rigorously derive bounds for specific Toeplitz determinants involving logarithmic coefficients pertaining to classes of convex and starlike functions concerning symmetric points. Furthermore, we present illustrative examples showcasing the sharpness of these established bounds. Our findings represent a substantial contribution to the advancement of our understanding of logarithmic coefficients and their profound implications across diverse mathematical contexts. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Some new results of difference perfect functions in topological spaces.
- Author
-
Bani-Ahmad, Feras, Alsayyed, Omar, and Atoom, Ali A.
- Subjects
TOPOLOGICAL spaces ,SET theory ,MATHEMATICAL symmetry ,HAUSDORFF spaces ,ANALYTIC functions - Abstract
Everyday problems are characterized by voluminous data and varying levels of ambiguity. Thereupon, it is critical to develop new mathematical approaches to dealing with them. In this context, the perfect functions are anticipated to be the best instrument for this purpose. Therefore, we investigate in this paper how to generate perfect functions using a variety of set operators. Symmetry is related to the interactions among specific types of perfect functions and their classical topologies. We can explore the properties and behaviors of classical topological concepts through the study of sets, thanks to symmetry. In this paper, we introduce a novel class of perfect functions in topological spaces that we term D-perfect functions and analyze them. Additionally, we establish the links between this new class of perfect functions and classes of generalized functions. Furthermore, while introducing the herein proposed D-perfect functions and analyzing them, we illustrate this new idea, explicate the associated relationships, determine the conditions necessary for their successful application, and give examples and counter-examples. Alternative proofs for the Hausdorff topological spaces and the D-compact topological spaces are also provided. For each of these functions, we examine the images and inverse images of specific topological features. Lastly, product theorems relating to these concepts have been discovered. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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