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The central aim of the current paper is to delve into the radii of starlikeness and convexity for two distinct normalizations of the big q-Bessel function, both of which are analytic within the confines of the unit disk of the complex plane. Additionally, by demonstrating that both functions possess an infinite number of zeros, each of which is a real number, the infinite product representations for these functions are derived. It is crucial to highlight that the Laguerre-Pólya class of real entire functions, the Hadamard factorization theorem, and the Euler-Rayleigh inequalities are key components of this study. Finally, by applying the Euler-Rayleigh inequalities to the least positive zeros of the normalized big q-Bessel functions, tight bounds, both lower and upper, for the radii of starlikeness and convexity are derived in this study. [ABSTRACT FROM AUTHOR]

This manuscript extends the integral transform C β α [ φ ] (z) : = ∫ 0 z ( φ (ζ) ζ (1 - ζ) β ) α d ζ , α , β ∈ C , where φ is normalized analytic function, to the case of logharmonic mapping and study their univalence properties. This integral transform carries the well-known Alexander (i.e. C 0 1 ) and Cesáro (i.e. C 1 1 ) transforms. Following the idea of classical shear construction for harmonic mappings, we employ the shear construction for logharmonic mappings that is introduced by Liu and Ponnusamy in 2022 with a goal to generate logharmonic integrals of Cesáro type. In addition, intriguing relationships between harmonic and non-vanishing logharmonic integrals corresponding to the integral transforms C β α are established. [ABSTRACT FROM AUTHOR]

In this paper, we define a new class $ \mathcal{R}_{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $ of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janowski-type functions. Using the well-known Carathéodory's inequality for function with real positive parts and the Keogh-Merkes and Ma-Minda's in equalities, we determined the upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion. Then, we found an upper bound for the Fekete-Szegö functional for the functions in this family. Further, a similar result for the first two coefficients and for the Fekete-Szegő inequality have been done the function $ \mathcal{G}^{-1} $ when $ \mathcal{G}\in \mathcal{R} _{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $. Next, for the functions of these newly defined family we determine coefficient estimates, distortion bounds, radius problems, and the radius of starlikeness and close-to-convexity. The novelty of the results is that we were able to investigate basic properties of these new classes of functions using simple methods and these classes are connected with the new convolution operator and the Janowski functions.

The present study aims to investigate a majorization problem for a class of q-starlike functions and for the subclass S ∗ (χ) of starlike functions as well as to rectify certain previous results. For this goal, the valid form connected with Nehari's inequality for q-difference operators was presented. Further, our findings contribute to the novelty of the results of this topic by revealing new insights. In addition, our results with previous works have connected, drawing inspiration from existing papers. Also, several new implications of the main result expressed as corollaries were provided and advances in the studied topic were made. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to find the sufficient conditions for some subclasses of analytic functions associated with Mittag-Leffler functions to be in subclasses of spiral-like univalent functions. Further, we discuss geometric properties of an integral operator related to Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

In this paper, we define a new class R t , δ , υ m , n , σ (A , B) of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janowski-type functions. Using the well-known Carathéodory's inequality for function with real positive parts and the Keogh-Merkes and Ma-Minda's in equalities, we determined the upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion. Then, we found an upper bound for the Fekete-Szegö functional for the functions in this family. Further, a similar result for the first two coefficients and for the Fekete-Szegő inequality have been done the function G − 1 when G ∈ R t , δ , υ m , n , σ (A , B) . Next, for the functions of these newly defined family we determine coefficient estimates, distortion bounds, radius problems, and the radius of starlikeness and close-to-convexity. The novelty of the results is that we were able to investigate basic properties of these new classes of functions using simple methods and these classes are connected with the new convolution operator and the Janowski functions. [ABSTRACT FROM AUTHOR]

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]

In this paper, we shall find the order of starlikeness and convexity for integral operators Fαj,βj,λj,ζ (z) = {ζ ∫0z tζ−1 πnj=1 (Eαj,βj(t)/t )1/λj dt}1/ζ, where the functions Eαj,βj are the normalized Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

Using Chebyshev polynomials and q-differential operator, we introduce a novel class of bi-univalent functions within the open unit disk. Initial coefficient bounds for this class are established, emphasizing their significance in complex analysis. Analyticity ensures the representation of these functions through convergent power series, offering a robust tool for comprehending their behavior. The condition of univalence guarantees the one-to-one nature of these functions, preventing multiple mappings of the same point. Researchers employ bi-univalent functions to delve into diverse aspects of complex analysis, unraveling their properties and applications across various mathematical contexts. The exploration encompasses the investigation of geometric properties, including Fekete-Szegö inequality and coefficient bounds, unraveling the intricate interplay between analytic and geometric characteristics. In summary, the study of bi-univalent functions contributes to the depth of complex analysis, providing a nuanced understanding of the relationships between analyticity and univalence. This exploration lays the foundation for advancements in mathematical theory and applications. [ABSTRACT FROM AUTHOR]

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]

In this study, we introduce the new subclasses, M α (sin) and M α (cos) , of α -convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of the Zalcman functional for the class M α (cos) for the case n = 3 , proving that the Zalcman conjecture holds for this value of n. Moreover, the problem of the Fekete–Szegő functional estimate for these classes is studied. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc U = {z: z ∈ C and |z| < 1}. We find the bounds on the initial coefficients |c2| and |c3| and upper bounds for the Fekete-Szego functional for the functions in this class. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ \left\vert A_{2}\right\vert $ and $ \left\vert A_{3}\right\vert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.

In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc U: For this subclass of functions, estimates of the initial coefficients |A2| and |A3| of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases. [ABSTRACT FROM AUTHOR]

In this paper, we consider convolution operator... discuss some interesting applications of these operators by introducing several new subclasses of analytic functions. Also geometric properties are investigated for integral operators on new subclasses of analytic functions and some subordination results are discussed for differential operator Dmλ,x. [ABSTRACT FROM AUTHOR]

The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized kk-Bessel functions, such as the radii of uniform convexity and of α\alpha -convexity. In addition, we show that the radii of α\alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α∈[0,1],\alpha \in {[}0,1], and they are decreasing with respect to the parameter α.\alpha . The key tools in the proof of our main results are infinite product representations for normalized kk-Bessel functions and some properties of real zeros of these functions.

In view of the subclass S L * (β) , which for β = 0 reduces to the class S L * , two more subclasses C L (β) and G L (β) are introduced. For all these three subclasses, we investigate upper bounds of second Hankel and second inverse Hankel determinates. In most of the cases, the results are sharp. [ABSTRACT FROM AUTHOR]

We introduce and examine two new subclass of bi-univalent function Σ , defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some new subclasses of analytic functions in the open unit disk U with negative coefficients defined by generalized Alexander integral operator. The aim of the present paper is to determine coefficient inequalities, inclusion relations, neighborhoods, partial sums and integral means properties for functions f belonging to these subclasses. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to determine the radii of starlikeness and convexity of the generalized k-Bessel functions for three different kinds of normalization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre–Pólya class plays a significant role in this paper. Moreover, the interlacing properties of the zeros of the k-Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler–Rayleigh inequalities for the real zeros of the generalized k-Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero. [ABSTRACT FROM AUTHOR]

In this article, we make use of the q-binomial theorem to introduce and study two new subclasses ℵ (α q , q) and ℵ (α , q) of meromorphic functions in the open unit disk U , that is, analytic functions in the punctured unit disk U ∗ = U \ { 0 } = { z : z ∈ C and 0 < z < 1 }. We derive inclusion relations and investigate an integral operator that preserves functions which belong to these function classes. In addition, we establish a strict inequality involving a certain linear convolution operator which we introduce in this article. Several special cases and corollaries of our main results are also considered. [ABSTRACT FROM AUTHOR]

Determining the sharp bounds for coefficient-related problems that appear in the Taylor–Maclaurin series of univalent functions is one of the most difficult aspects of studying geometric function theory. The purpose of this article is to establish the sharp bounds for a variety of problems, such as the first three initial coefficient problems, the Zalcman inequalities, the Fekete–Szegö type results, and the second-order Hankel determinant for families of Sakaguchi-type functions related to the cardioid-shaped domain. Further, we study the logarithmic coefficients for both of these classes. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate the Sălăgean - type probability distribution of order α. In this paper, we obtain moments, factorial moments and moment generating function for this distribution. Finally, we obtain a entropy of this distribution. Our results improve and generalize the results of Porwal [Starlike and convex type probability distribution, Afr. Mat. 30 (2019)].

In the present paper we study a majorization problem for a class of analytic functions of α-convex functions defined by subordination with respect to a given function φ. In a special case we obtain the majorization problem for the class M(α) of α-convex functions. Further, coefficient bounds for some majorized functions are estimated. [ABSTRACT FROM AUTHOR]

In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator D r . We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which D r l ′ (z) ϑ z D r l ′ (z) D r l (z) 1 − ϑ ≺ e z   (0 ≤ ϑ ≤ 1) lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a q-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.

We have introduced a comprehensive subclass of analytic functions with respect to (j; k) - symmetric points. We have obtained the interesting coefficient bounds for the newly defined classes of functions. Further, we have extended the study using quantum calculus. Our main results have several applications, here we have presented only a few of them. [ABSTRACT FROM AUTHOR]

We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with the q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for functions in these classes. This paper generalizes some known results, as well as provides some new ones. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new subclasses ... and of analytic functions in the open unit disk with negative coefficients defined by generalized Mittag-Leffler function. The object of the present paper is to determine coefficient inequalities, inclusion relations and neighborhoods properties for functions belonging to these subclasses. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate the Sălăgean - type probability distribution of order α. In this paper, we obtain moments, factorial moments and moment generating function for this distribution. Finally, we obtain a entropy of this distribution. Our results improve and generalize the results of Porwal. [ABSTRACT FROM AUTHOR]

In this research article, making use of Erdelyi-Kober integral operator, we define a new subclass T a, c μ (α, β, γ, A,B) of starlike functions with negative coefficient. Various properties like coefficient estimates, neighbourhood results, integral means, partial sums and subordination results are examined for this class. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new subclass of analytic functions defined by $\mathcal{D}^{k}\mathcal{L} _{a}^{\delta }f(z)$ differential operator in the unit disk. For this subclass, the Fekete-Szegö type coefficient inequalities are derived.

Abstract We consider a family of analytic and normalized functions with the property that zf′(z)/f(z) $zf'(z)/f(z)$ (or 1+zf″(z)/f′(z) $1+zf''(z)/f'(z)$) lies in a domain bounded by a right branch of a hyperbola ρ=ρ(s)=(2cosφs)−s $\rho =\rho (s)= ( 2 \cos \frac{\varphi }{s} )^{-s}$, where 0

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Recently considerable effort has been devoted to the study of fractional calculus in many branches of mathematics and physics. The main object of the present investigation is to provide a brief survey concerning fractional integral and derivative operators in Geometric Function Theory. The generalizations of these operators are also concerned along with numerous properties of these generalized operators. We also list some samples which reflect our recent investigations in the Geometric Function Theory. [ABSTRACT FROM AUTHOR]

We find an unifying approach to the analytic representation of the domain bounded by a generalized Pascal snail. Special cases as the Pascal snail, Both leminiscate, conchoid of the Sluze and a disc are included. The behaviour of functions related to generalized Pascal snail is studied. [ABSTRACT FROM AUTHOR]

The aim of the present study is to find the essential properties for some subclasses of analytic functions which are related to Poisson distribution that are member of the classes of spiral-like univalent functions. Further, we studied inclusion relations for such subclasses, and also we determined some properties of an integral operator related to Poisson distribution series. Several corollaries and consequences of the main results are also considered. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to find the radii of starlikeness and convexity of the Ramanujan type function for three different kinds of normalization by using their Mittag–Leffler expansion in such a way that the resulting functions are analytic in the unit disk of the complex plane. A result of Zhang (Proc Am Math Soc 145:241–250, 2017) on the reality of the zeros of Ramanujan type entire functions play important roles in this paper. Moreover, the interlacing properties of the zeros of Ramanujan type functions and its derivative are also useful in the proof of the main results. In addition, by using the Euler–Rayleigh inequalities, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the Ramanujan type entire functions. Finally, we give monotonicity and Redheffer-type inequalities for this function. [ABSTRACT FROM AUTHOR]

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

In this paper, we show that the Carathéodory function φ Ne (z) = 1 + z - z 3 / 3 maps the open unit disk D onto the interior of the nephroid, a 2-cusped kidney-shaped curve, (u - 1) 2 + v 2 - 4 9 3 - 4 v 2 3 = 0 , and introduce new Ma–Minda-type function classes S Ne ∗ and C Ne associated with it. Apart from studying the characteristic properties of the region bounded by this nephroid, the structural formulas, extremal functions, growth and distortion results, inclusion results, coefficient bounds and Fekete–Szegö problems are discussed for the classes S Ne ∗ and C Ne . Moreover, for β ∈ R and some analytic function p(z) satisfying p (0) = 1 , we prove certain subordination implications of the first-order differential subordination 1 + β z p ′ (z) / p j (z) ≺ φ Ne (z) , j = 0 , 1 , 2 , and obtain sufficient conditions for some geometrically defined function classes available in the literature. [ABSTRACT FROM AUTHOR]

In this work, bi-univalent functions, which are one of the most important research areas of Geometric Function Theory and which are still very popular in recent years, have been investigated. For the studies of functions, it is customary to determine the bound. In this direction, firstly, we introduce a new subclass of bi-univalent functions in the open unit disk D = {z ∈ C: /z/ < 1}. For this purpose, the Komatu integral operator developed for complex functions and subordination princible are used. Afterwards, the relation between the Fibonacci number sequence and the functions with the positive real part is given. This relation is a fundamental role for Results section. The upper bounds of the first two Taylor-Maclaurin coefficients are investigated. Finally, we derive Fekete-Szegö inequalities for functions belonging to this newly-defined class. The obtained results are compared with studies in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study two new subclasses 𝒯 𝒮 m ∗ (α , λ) and 𝒯 𝒞 m (α , λ) of analytic functions which are defined by means of a differential operator. Some results connected to partial sums and neighborhoods and integral means related to these subclasses are obtained. [ABSTRACT FROM AUTHOR]

We consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation 1 ρ = 2 cos ⁡ φ s s (0 < s ≤ 1 , | φ | < (π s) / 2). $\begin{array}{} \frac{1}{\rho}=\left(2\cos\frac{\varphi}{s}\right)^s\quad (0 \lt s\le 1,\, |\varphi| \lt (\pi s)/2). \end{array}$ We mainly study a coefficient problem of the families of functions for which zf′/f or 1 + zf″/f′ map the unit disk onto a subset of ℍ(s). We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.

In this paper, we introduce and investigate new subclasses (Yamakawa-type bi-starlike functions and another class of Lashin, both mentioned in the reference list) of bi-univalent functions defined in the open unit disk, which are associated with the Gegenbauer polynomials and satisfy subordination conditions. Furthermore, we find estimates for the Taylor–Maclaurin coefficients |a2| and |a3| for functions in these new subclasses. Several known or new consequences of the results are also pointed out.

In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated.

In this paper, two new integral operators are defined using the operator DRλm,n, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator DRλm,n are also obtained.