7,740 results
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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]
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- 2024
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3. Moduli difference of successive inverse coefficients for certain classes of close-to-convex functions
- Author
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Kumar, Virendra
- Published
- 2024
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4. 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]
- Published
- 2024
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5. 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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6. Smooth solutions to the heat equation which are nowhere analytic in time.
- Author
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Yang, Xin, Zeng, Chulan, and Zhang, Qi S.
- Subjects
ANALYTIC spaces ,ANALYTIC functions ,HEAT equation - Abstract
The existence of smooth but nowhere analytic functions is well-known (du Bois-Reymond [Math. Ann. 21 (1883), no. 1, pp. 109–117]). However, smooth solutions to the heat equation are usually analytic in the space variable. It is also well-known (Kowalevsky [Crelle 80 (1875), pp. 1–32]) that a solution to the heat equation may not be time-analytic at t=0 even if the initial function is real analytic. Recently, it was shown by Dong and Pan [J Math. Fluid Mech. 22 (2020), no. 4, Paper No. 53]; Dong and Zhang [J. Funct. Anal. 279 (2020), no. 4, Paper No. 108563]; Zhang [Proc. Amer. Math. Soc. 148 (2020), no. 4, pp. 1665–1670] that solutions to the heat equation in the whole space, or in the half space with zero boundary value, are analytic in time under an essentially optimal growth condition. In this paper, we show that time analyticity is not always true in domains with general boundary conditions or without suitable growth conditions. More precisely, we construct two bounded solutions to the heat equation in the half plane which are nowhere analytic in time. In addition, for any \delta >0, we find a solution to the heat equation on the whole plane, with exponential growth of order 2+\delta, which is nowhere analytic in time. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Providing the optimal method for sport places site selection based on GIS analytic functions
- Author
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Salimi, Mehdi and Khodaparst, Mahboubeh
- Published
- 2021
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8. Second Hankel Determinant For Bazilevic Functions Subordinate To k-Fibonacci sequence.
- Author
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Pulala, Sumalatha, Sharma, R. B., and Haripriya, M.
- Subjects
STAR-like functions ,FIBONACCI sequence ,ANALYTIC functions ,DETERMINANTS (Mathematics) ,EMPLOYEES ,PAPER arts - Abstract
In this present investigation, we introduce a new subclass of analytic functions which is denoted by B
k β , (β ≥ 0) for this class we obtain sharp upper bounds for the second Hankel determinant and the Fekete-Szegö inequality in the open unit disc D, subordinate to k-Fibonacci sequence. The results of this paper generalize the work done by earlier researchers in this direction. [ABSTRACT FROM AUTHOR]- Published
- 2019
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9. Temperature dependence of rate constant of OSEE of gamma irradiated exo- sensitive paper with CaSO$sub 4$ and graphite
- Author
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Bohun, A [ed.]
- Published
- 1973
10. 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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11. 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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12. 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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13. A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials
- Author
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Eie, Minking
- Published
- 1996
14. HARDY SPACES OF CERTAIN CLASSES OF ANALYTIC FUNCTIONS.
- Author
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Varma, S. Sunil and Johnson, Jocelyn
- Subjects
HARDY spaces ,UNIVALENT functions ,FUNCTION spaces ,RESEARCH personnel ,INTEGRALS ,ANALYTIC functions - Abstract
In this paper we consider various subclasses of normalized, analytic functions defined in the open unit disk A = {z = C : z < 1} in the complex plane C and study the Hardy space of the functions in these subclasses. This study provides an analysis of the growth of these functions near the boundary of the open unit disk and the Taylor's coefficients of them. The study is carried out using the methods of integral means and subordination of analytic functions. Determination of explicit indices of the Hardy space and order of the growth rate of the Taylor coefficient of these functions are important results here. The novelty of the work here is an attempt to extend the study of the above mentioned features for functions in standard subclasses of analytic univalent functions which were not considered by researchers in the past. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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15. ESTIMATES ON INITIAL COEFFICIENT BOUNDS OF SUBCLASSES OF BI-UNIVALENT FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR.
- Author
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Shelake, Girish D., Nilapgol, Sarika K., and Joshi, Santosh B.
- Subjects
ANALYTIC functions ,DIFFERENTIAL operators ,UNIVALENT functions ,TERMS & phrases - Abstract
In this present paper, we introduce two new subclasses HkΣ (α, δ, λ, µ, σ) and HkΣ (β, δ, λ, µ, σ) of normalized analytic bi-univalent functions defined in the open unit disk and associated with generalized differential operator. Further, we obtain bounds for the second and third Taylor- Maclaurin coefficients of the functions of these subclasses. Also, we obtain some consequences of results obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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16. 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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17. 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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18. COMPUTATION OF TWO-DIMENSIONAL STOKES FLOWS VIA LIGHTNING AND AAA RATIONAL APPROXIMATION.
- Author
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YIDAN XUE, WATERS, SARAH L., and TREFETHEN, LLOYD N.
- Subjects
STOKES flow ,FLUID flow ,LIGHTNING ,REYNOLDS number ,ANALYTIC functions ,ANALYTICAL solutions - Abstract
Low Reynolds number fluid flows are governed by the Stokes equations. In two dimensions, Stokes flows can be described by two analytic functions, known as Goursat functions. Brubeck and Trefethen [SIAM J. Sci. Comput., 44 (2022), pp. A1205-A1226] recently introduced a lightning Stokes solver that uses rational functions to approximate the Goursat functions in polyg- onal domains. In this paper, we present the LARS algorithm (lightning-AAA rational Stokes) for computing two-dimensional (2D) Stokes flows in domains with smooth boundaries and multiply con- nected domains using lightning and AAA rational approximation [Y. Nakatsukasa, O. Sète, and L. N. Trefethen, SIAM J. Sci. Comput., 40 (2018), pp. A1494-A1522]. After validating our solver against known analytical solutions, we solve a variety of 2D Stokes flow problems with physical and engineering applications. Using these examples, we show rational approximation can now be used to compute 2D Stokes flows in general domains. The computations take less than a second and give solutions with at least 6-digit accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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19. 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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20. 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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21. 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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22. Conformable fractional derivative in commutative algebras.
- Author
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Shpakivskyi, Vitalii S.
- Subjects
FUNCTION algebras ,MONOGENIC functions ,ASSOCIATIVE algebras ,CLIFFORD algebras ,COMMUTATIVE algebra ,ALGEBRA ,ANALYTIC functions - Abstract
In this paper, an analog of the conformable fractional derivative is defined in an arbitrary finite-dimensional commutative associative algebra. Functions taking values in the indicated algebras and having derivatives in the sense of a conformable fractional derivative are called φ-monogenic. A relation between the concepts of φ-monogenic and monogenic functions in such algebras has been established. Two new definitions have been proposed for the fractional derivative of the functions with values in finite-dimensional commutative associative algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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23. 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
- View/download PDF
24. 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
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25. 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
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26. On simultaneous similarity of families of commuting operators.
- Author
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Kouchekian, Sherwin and Shekhtman, Boris
- Subjects
BANACH spaces ,LINEAR algebra ,ANALYTIC spaces ,FUNCTION spaces ,ANALYTIC functions - Abstract
Characterization of simultaneous similarity for commuting m- tuples of operators is an open problem even in finite-dimensional spaces; known as "A wild problem in linear algebra". In this paper we offer a criterion for simultaneous similarity of m-tuples of k-cyclic commuting operators on an arbitrary Banach space. Moreover, we obtain an additional equivalence condition in the case of finite dimensional Banach spaces, which extends the result found by Shekhtman [Math. Stat. 1 (2013), pp. 157–161] for pairs of cyclic commuting matrices. We also present two applications of our results, one in the case of general multiplication operators on Banach spaces of analytic function, and one for m-tuples of commuting square matrices. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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27. THE SHARP BOUNDS OF THE HANKEL DETERMINANTS FOR THE CLASS OF CONVEX FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS.
- Author
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RATH, BISWAJIT, KUMAR, K. SANJAY, KRISHNA, D. VAMSHEE, and VISWANADH, G. K. SURYA
- Subjects
SYMMETRIC functions ,CONVEX functions ,HANKEL functions ,ANALYTIC functions ,DETERMINANTS (Mathematics) - Abstract
In this paper, we estimate sharp bounds for certain Hankel determinants, H
2,3 (f), H3,1 (f) and Zalcman functional |a²3 -- a5 | for the class of convex function with respect to symmetric points, hence proving the recent conjecture made by Virendra et al., that affirms the sharp bound for the third Hankel determinant in the classes of convex functions with respect to symmetric points is 4/135. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
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28. 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
29. New definitions of fractional derivatives and integrals for complex analytic functions.
- Author
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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
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30. 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
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31. Differentiation Formulas for Analytic Functions
- Author
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Lyness, J. N.
- Published
- 1968
- Full Text
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32. 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
- View/download PDF
33. 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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34. Some Classes of Bazilevič-Type Close-to-Convex Functions Involving a New Derivative Operator.
- Author
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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
35. 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
36. 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
37. Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials.
- Author
-
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
38. 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
39. Note on bounds on the coefficients of a subclass of m-fold symmetric bi-univalent functions.
- Author
-
Zireh, Ahmad, Hajiparvaneh, Saideh, and Bulut, Serap
- Subjects
- *
UNIVALENT functions , *SYMMETRIC functions , *ANALYTIC functions - Abstract
In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions which both f (z) and f - 1 (z) are m-fold symmetric on the open unit disk. Furthermore, we find upper bounds for the initial coefficients | a m + 1 | and | a 2 m + 1 | for functions in this subclass. The results presented in this paper generalize and improve some recent works [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. On universality in short intervals for zeta-functions of certain cusp forms.
- Author
-
Laurinčikas, Antanas and Šiaučiūnas, Darius
- Subjects
LIMIT theorems ,ZETA functions ,MODULAR groups ,ANALYTIC functions ,ANALYTIC spaces ,MODULAR forms ,CUSP forms (Mathematics) - Abstract
In this paper, we consider universality in short intervals for the zeta-function attached to a normalized Hecke-eigen cusp form with respect to the modular group. For this, we apply a conjecture for the mean square in short interval on the critical strip for that zeta-function. The proof of the obtained universality theorem is based on a probabilistic limit theorem in the space of analytic functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Connections between various subclasses of planar harmonic mappings involving Mittag-Leffler functions.
- Author
-
Taşar, Naci, Sakar, F. Mūge, and Frasin, Basem Aref
- Abstract
In this existing paper, we examine a connection between certain class of harmonic univalent functions with starlike and convex harmonic functions define in the open unit disk by applying the convolution operator defined by Mittag-Leffler function. Several corollaries and consequences of the main results are also obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Results for Analytic Function Associated with Briot–Bouquet Differential Subordinations and Linear Fractional Integral Operators.
- Author
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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
43. 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
44. A subclass of analytic functions with negative coefficient defined by generalizing Srivastava-Attiya operator.
- Author
-
Hamaad, Suha J., Juma, Abdul Rahman S., and Ebrahim, Hassan H.
- Subjects
- *
ANALYTIC functions , *CONVEX functions , *GENERALIZATION - Abstract
The primary goal of this paper is to introduce and investigate a novel subclass of analytic functions in the open unit disk by generalizing the Srivastava-Attiya operator. So by using the generalization we have introduced a subclass of analytic function with negative coefficients in the unit disk. We have referred to the previous studies that used the Sirvastava-Attiya operator and generalized it, explained the functions of the class 퓐 and the basic definitions that included this paper. We used some important lemmas from previous studies to prove our results, and we obtained some important geometric properties of the analytical functions. We proved the theorem of growth and destortion, and we showed the cofficient bound, extreme points of the functions in this class, in addition to the radii of the starlike, convex and close-to-convex functions of order 휑. Finally, we defined the 훼 −neighborhood and showed the relationship between the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ (γ , ρ , l , σ) and the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ , ω (γ , ρ , l , σ). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Λ-separately subharmonic functions.
- Author
-
Imomkulov, Sevdiyor, Abdikadirov, Sultanbay, and Sharipov, Rasul
- Subjects
- *
SUBHARMONIC functions , *DIFFERENTIAL forms , *HARMONIC functions , *ANALYTIC functions - Abstract
One of the important problems of potential theory is the study of (sub) harmonicity of separately (sub) harmonic functions. This problem has been studied by many authors and fairly complete results have been obtained. In this paper we will give a survey of results in this area and study a → -separately subharmonic functions. In this paper, we assume that all coefficients of differential forms belong to the class С1, unless additional smoothness conditions are required. We give a definition of Λ-separately subharmonic function, where Λ=(α′,α″) and we show that under additional conditions, these functions belongs to the class α-subharmonic functions, where a = a ′ (z) ∧ a ′ ′ (w) ∧ β , β = d d c ( | z | 2 + | w | 2). If the function u(z, w)∈С2 (D × G) is ∧−separately subharmonic, then by the set of variables ddcu(z, w) ∧α(z, w) ≥0, i.e. the function u(z, w) is α-subharmonic, where a (z , w) = a ′ (z) ∧ a ′ ′ (w) ∧ β , β = d d c ( | z | 2 + | w | 2). If a function u (z, w), (z, w) ∈ D×G is Λ-separately harmonic and coefficients of differential forms α′(z) and α″(w) are real analytic in the domains D and G respectively, then u(z, w) is real analytic α−harmonic function (where α=α′(z) ∧α″(w)∧β) in the domain D×G by the set of variables. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Non-tangential boundary values for A(z)−analytic functions.
- Author
-
Husenov, Behzod
- Subjects
- *
ANALYTIC functions - Abstract
We consider A(z)−analytic functions in case when A(z) is anti-analytic function. This article introduces Lp classes of A(z)−analytics functions by p ≥ 1. In this paper, we introduce for a non-tangential boundary value of the A(z)−analytic function. Thus, this paper proves Fatou's theorem on non-tangential values for A(z)−analytic functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values.
- Author
-
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
48. On the logarithmic coeffcients for some classes defined by subordination.
- Author
-
Adegani, Ebrahim Analouei, Alimohammadi, Davood, Bulboacă, Teodor, Nak Eun Cho, and Bidkham, Mahmood
- Subjects
LOGARITHMIC functions ,ANALYTIC functions ,UNIVALENT functions - Abstract
The logarithmic coeffcients of univalent functions play an important role in different estimates in the theory of univalent functions. In this paper, due to the significant importance of the study of these coeffcients, we find the upper bounds for some expressions associated with the logarithmic coeffcients of functions that belong to some classes defined by using the subordination. Moreover, we get the best upper bounds for the logarithmic coeffcients of some subclasses of analytic functions defined and studied in many earlier papers. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Convergence analysis of Laguerre approximations for analytic functions.
- Author
-
Wang, Haiyong
- Subjects
ANALYTIC functions ,PARABOLA ,INTERPOLATION ,INTEGRALS ,ALGORITHMS ,LAPLACE transformation - Abstract
Laguerre spectral approximations play an important role in the development of efficient algorithms for problems in unbounded domains. In this paper, we present a comprehensive convergence rate analysis of Laguerre spectral approximations for analytic functions. By exploiting contour integral techniques from complex analysis, we prove that Laguerre projection and interpolation methods of degree n converge at the root-exponential rate O(\exp (-2\rho \sqrt {n})) with \rho >0 when the underlying function is analytic inside and on a parabola with focus at the origin and vertex at z=-\rho ^2. As far as we know, this is the first rigorous proof of root-exponential convergence of Laguerre approximations for analytic functions. Several important applications of our analysis are also discussed, including Laguerre spectral differentiations, Gauss-Laguerre quadrature rules, the scaling factor and the Weeks method for the inversion of Laplace transform, and some sharp convergence rate estimates are derived. Numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Spectrum of banach valued holomorphic functions and polar sets.
- Author
-
Taki, Zakaria and Nokrane, Abdelkrim
- Subjects
SET functions ,BANACH algebras ,HOLOMORPHIC functions ,ANALYTIC functions - Abstract
Let A be a complex unital Banach algebra and D be a non-empty open connected subset of C. Let f be a holomorphic A-valued function on D. We set: ∑(f) = {z ∈ D | f(z) ∉ ∈ Inv(A)}, where Inv(A) is the set of all invertible elements in A. In this paper, we give a description of ∑(f) using the classical spectrum of f(z) (z ∈ D). Moreover, within the framework of this paper, we give a partial positive answer to the following problem which was posed by B. Aupetit: If the usual spectrum σ(f(z)) is polar for all z ∈ D, is it true that ∑(f) is polar? [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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