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The authors propose to investigate some new criteria for a certain class of meromorphically strongly starlike functions in the punctured open unit disk. Some intriguing applications that arise as special cases of the main results, which are presented in this study, are also considered.

The authors propose to investigate some new criteria for a certain class of meromorphically strongly starlike functions in the punctured open unit disk. Some intriguing applications that arise as special cases of the main results, which are presented in this study, are also considered. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study a new q-fractional integral operator which essentially stems from a successive application of the Srivastava-Owa operator of fractional integration with the q-Ruscheweyh derivative operator. As an application of this new q-fractional integral operator, we investigate a coefficient problem involving the second Hankel determinant H²2(f) for normalized analytic and univalent functions f(z) belonging to some normalized families of q-starlike and q-convex functions in the open unit disk U. [ABSTRACT FROM AUTHOR]

In most cases, the problem of finding bounds for the inverse function is much more difficult than finding bounds for the function itself. Thus, there are relatively little sharp bounds of Hankel determinant on the inverse functions. In the present paper, we introduce a subclass of bounded turning function Rcar associated with a cardioid domain. The purpose of this article is to investigate certain coefficient related problems on the inverse functions for f ∈ Rcar. The bounds of some initial coefficients, the Fekete-Szego type inequality and the estimation of Hankel determinants of second and third order are obtained. All of these bounds are proved to be sharp. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce a new subclass HΣ(δ, λ, m, θ, x) of analytic and bi-univalent functions by using the Horadam polynomials, which is associated with the Pascal distribution series and to investigate the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we obtain the Fekete-Szeg¨o inequality for functions in the class HΣ(δ, λ, m, θ, x) which we have introduced here. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a certain class H λ,a m,q (ξ,M) of normalized analytic functions of complex order connected with a q-analogue of integral operators. For this complex-order analytic function class, we determine a sufficient condition in terms of the coefficients, estimates for the coefficients and a maximization theorem concerning the coefficients. Various consequences and applications of our main results are also considered. A brief remark about the demonstrated equivalence of the q-calculus and the so-called (p,q)-calculus is also presented. [ABSTRACT FROM AUTHOR]

Let S B ∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ be the class of normalized starlike functions associated with a function related to the Bell numbers. By establishing bounds on some coefficient functionals for the family of functions with positive real part, we derive for functions in the class S B ∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants. Bounds on the first three consecutive higher-order Schwarzian derivatives for functions in the class S B ∗ $\begin{array}{} \mathcal{S}^*_B \end{array}$ are investigated. [ABSTRACT FROM AUTHOR]

By using a linear operator associated with the λ-generalized Hurwitz-Lerch zeta function, which is defined here by means of the Hadamard product (or convolution), the authors introduce and investigate certain sufficient conditions for these meromorphic functions to satisfy a subordination. In fact, these results extend known results of starlikeness, convexity, and close to convexity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study some subclasses of p-valently analytic functions in the open unit disk U by applying the q-derivative operator and the fractional q-derivative operator in conjunction with the principle of subordination between analytic functions. For the Taylor-Maclaurin coefficients ... of each of these subclasses of p-valently analytic functions, we derive sharp bounds for the Fekete-Szegő functional given by ... Relevant connections of the results presented in this paper with those derived in earlier works are also considered. [ABSTRACT FROM AUTHOR]

By using a linear operator associated with the λ-generalized Hurwitz-Lerch zeta function, which is defined here by means of the Hadamard product (or convolution), the authors introduce and investigate certain sufficient conditions for this meromorphic functions to satisfy a subordination. In fact, these results extend known results of star- likeness, convexity, and close to convexity. [ABSTRACT FROM AUTHOR]

Studies of convolution play an important role in Geometric Function Theory (GFT). Such studies attracted a large number of researchers in recent years. By making use of the Hadamard product (or convolution), several new and interesting subclasses of analytic and univalent functions have been introduced and investigated in the direction of well-known concepts such as the subordination and superordination inequalities, integral mean and partial sums, and so on. In this article, we apply the Hadamard product (or convolution) by utilizing some special functions. Our contribution in this paper includes defining a new linear operator in the form of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright pΨq-function in the right-half of the open unit disk where where ℜ(z) > 0. We then show that the new linear convolution operator is bounded in some spaces. In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright pΨq-notation is used in our results. [ABSTRACT FROM AUTHOR]

In the present investigation, we obtain the estimates on the initial Taylor-Maclaurin coefficients for functions in two new subclasses of meromorphically bi-univalent functions defined on the domain Δ given by Δ = {Z : z ∈ ℂ and 1 < |z| < ∞}. Several other closely-related earlier results are also indicated. [ABSTRACT FROM AUTHOR]

There are many articles in the literature dealing with the first-order and the second-order differential subordination and differential superordination problems for analytic functions in the unit disk, but there are only a few articles dealing with the third-order differential subordination problems. The concept of third-order differential subordination in the unit disk was introduced by Antonino and Miller, and studied recently by Tang and Deniz. Let $$\Omega $$ be a set in the complex plane $$\mathbb {C}$$ , let $$\mathfrak {p}(z)$$ be analytic in the unit disk $$\mathbb {U}=\{z:z\in \mathbb {C}\quad \text {and} \quad |z|<1\}$$ , and let $$\psi : \mathbb {C}^4\times \mathbb {U}\rightarrow \mathbb {C}$$ . In this paper, we investigate the problem of determining properties of functions $$\mathfrak {p}(z)$$ that satisfy the following third-order differential superordination: As applications, we derive some third-order differential superordination results for analytic functions in $$\mathbb {U}$$ , which are associated with a family of generalized Bessel functions. The results are obtained by considering suitable classes of admissible functions. New third-order differential sandwich-type results are also obtained. [ABSTRACT FROM AUTHOR]

In the present investigation, we consider a new subclass Σ(τ,γ,φ)of the class R consisting of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class Σ(τ,γ,φ)introduced here, we obtain estimates on the first two Taylor-Maclaurin coefficients ∣a2∣ and ∣a3∣. Several related classes of analytic and bi-univalent functions in U are also considered and connections to some of the earlier known results are pointed out. [ABSTRACT FROM AUTHOR]

Let ∑ denote the class of functions belonging to the normalized analytic function class A in the open unit disk U, which are bi-univalent in U, that is, both the function f and its inverse f-1 are univalent in U. The usual method for computation of the coefficients of the inverse function f-1(z) by means of the relation f-1(f(z))= z is too difficult to apply in the case of m-fold symmetric analytic functions in U. Here, in our present investigation, we aim at overcoming this difficulty by using a general formula to compute the coefficients of f-1(z) in conjunction with the residue calculus. As an application, we introduce two new subclasses of the bi-univalent function class ∑ in which both f(z) and f-1(z) are m-fold symmetric analytic functions with their derivatives in the class P of analytic functions with positive real part in U. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |am+1| and |a2m+1j|. [ABSTRACT FROM AUTHOR]

By making use of iterations of the Owa-Srivastava fractional derivative operator, two new classes of analytic functions are introduced and investigated systematically. Several basic properties of functions belonging to each of these two classes of analytic functions such as inclusion theorems, subordination theorems, growth theorems and class-preserving transforms are studied. [ABSTRACT FROM AUTHOR]

Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator. [ABSTRACT FROM AUTHOR]

Strong differential subordination and superordination properties are determined on the Liu-Srivastava operator (which, just as the relatively more familiar Dziok-Srivastava operator, is defined by using a generalized hypergeometric function) for some families of multivalently meromorphic functions in the punctured open unit disk by investigating appropriate classes of admissible functions. New strong differential sandwich-type results for the Liu-Srivastava operator are also obtained. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some subordination and superordination implications associated with a class of fractional differintegral operators, which are obtained by considering suitable classes of admissible multivalent analytic functions. The sandwich-type theorems for these operators are also considered. [ABSTRACT FROM AUTHOR]

Let Ap (p∈:={1, 2, 3, ...}) be the class of functions f given by [image omitted] which are analytic in the open unit disk . Making use of the method of differential subordinations, we obtain some sufficient conditions for f(z)∈Ap involving the Dziok-Srivastava operator to satisfy certain subordination properties. The results presented here are shown not only to generalize the main results in several earlier investigations, but also to give rise to many other new results. [ABSTRACT FROM AUTHOR]

The main object of this article is to introduce and investigate an integral operator Js, b(f) defined, by using the Hurwitz-Lerch Zeta function, on the various subclasses of the class of normalized analytic functions f in the open unit disk . Using the technique of differential subordination, an interesting property of the general integral operator Js, b(f) is obtained. Some applications of the results presented here are also considered. [ABSTRACT FROM AUTHOR]

In the present article, we obtain the subordination- and superordination-preserving properties of certain nonlinear integral operators defined on the space of normalized analytic functions in the open unit disk. A differential sandwich-type theorem for these integral operators is also presented. [ABSTRACT FROM AUTHOR]

The purpose of this article is to derive some subordination and superordination results for certain families of normalized analytic functions in the open unit disk, which are acted upon by a class of multiplier transformations. Relevant connections of the results, which are presented in this article, with various known results are also considered. [ABSTRACT FROM AUTHOR]

In this article, we investigate the mappings of various subclasses of univalent functions by means of certain families of integral operators. Especially, by using the norm estimates of the pre-Schwarzian derivatives, we determine conditions under which these integral operators have geometric meaning associated with the typical subclasses of analytic and univalent functions. [ABSTRACT FROM AUTHOR]

In Geometric Function Theory , it is well known that the familiar Koebe function f ( z ) = z /(1 - z ) 2 is the extremal function for the class &Sscr; * of starlike functions in the open unit disk &Uopf; and also that the function g ( z ) = z /(1 - z ) is the extremal function for the class &Kscr; of convex functions in the open unit disk &Uopf;. However, the partial sum f n ( z ) of f ( z ) is not starlike in &Uopf; and the partial sum g n ( z ) of g ( z ) is not convex in &Uopf;. The aim of the present paper is to investigate the starlikeness and convexity of these partial sums f n ( z ) and g n ( z ). Computational and graphical usages of Mathematica (Version 4.0) as well as geometrical descriptions of the image domains in several illustrative examples are also presented. * E-mail: owa@math.kindai.ac.jp [ABSTRACT FROM AUTHOR]

The authors investigate the subordination properties of a certain family of integral operators, which is defined here on the space of normalized analytic functions in the open-unit disk. An application of the main subordination theorem to the Gauss hypergeometric function is also considered. * E-mail: owa@math.kindai.ac.jp [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce a new subclass of meromorphic q-starlike functions which are associated with the Janowski functions. A characterization of meromorphically q-starlike functions associated with the Janowski functions has been obtained when the coefficients in their Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, partial sums, and the radius of starlikeness estimates for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we derive some bounds for the real parts and arguments of the functionals given by ... where Js;b is the widely-investigated Srivastava-Attiya operator defined on the class of normalized analytic functions f in the open unit disk ... with suitable real parameters s and b. These results reduce upon specialization to some well-known inclusion relationships for several classes of functions with given geometric properties. We also make a comparison between one of the results obtained here and an already known result for some specific cases. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate and present several sets of sufficient conditions for Carathéodory functions in the open unit disk U. We then apply the main results proven here in order to derive some conditions for starlike functions in U. Relevant connections with various known results are also considered. [ABSTRACT FROM AUTHOR]