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The research here was motivated by a number of recent studies on Hankel inequalities and sharp bounds. In this article, we define a new subclass of holomorphic convex functions that are related to tangent functions. We then derive geometric properties like the necessary and sufficient conditions, radius of convexity, growth, and distortion estimates for our defined function class. Furthermore, the sharp coefficient bounds, sharp Fekete-Szegö inequality, sharp 2nd order Hankel determinant, and Krushkal inequalities are given. Moreover, we calculate the sharp coefficient bounds, sharp Fekete-Szegö inequality, and sharp second-order Hankel determinant for the functions whose coefficients are logarithmic. [ABSTRACT FROM AUTHOR]

this paper, we introduce two interesting subclasses of meromorphic bi-univalent functions defined by Al-Oboudi differential operator. Estimates for the initial coefficients |c0|, |c1| and |c2| are obtained for the functions in these new subclasses. [ABSTRACT FROM AUTHOR]

Keeping in view the various important applications of Mittag-Leffer functions in the fields of applied sciences, we introduce Pascu-type analytic functions utilizing the concept of Mittag-Leffler functions in the region of Janowski domain. Moreover, we investigate some useful properties of these functions such as sufficiency criteria, distortion and growth bounds, convex combination, radius of starlikeness, and some partial sum results. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new subclass of analytic functions utilizing the idea of Mittag-Leffler type Poisson distribution associated with the Janowski functions. Further, we discuss some important geometric properties like necessary and sufficient condition, convex combination, growth and distortion bounds, Fekete-Szegö inequality, and partial sums for this newly defined class. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to apply the concepts of p , q -derivative by establishing a new subclass of analytic functions connected with symmetric circular domain. Further, we investigate necessary and sufficient conditions for functions belonging to this class. Convex combination, weighted mean, arithmetic mean, growth theorem, and convolution property are also determined. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to introduce the new subclass of analytic functions whose coefficients are Borel distributions in the Janowski domain. Further, we investigate some useful number of properties such as Fekete–Szegő inequality, necessary and sufficient condition, growth and distortion approximations, convex linear combination, arithmetic mean, radii of close-to-convexity and starlikeness and partial sums, followed by some extremal functions for this defined class. The symmetry properties and other properties of the subclass of functions introduced in this paper can be studied as future research directions. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function f, we obtain sufficient conditions for multivalent starlike functions connected with petal-shape domain. Finally, in the concluding section, we draw the attention of the interested readers toward the prospect of studying the basic or quantum (or q-) generalizations of the results, which are presented in this paper. However, the (p , q) -variations of the suggested q-results will provide a relatively minor and inconsequential development because the additional (rather forced-in) parameter p is obviously redundant. [ABSTRACT FROM AUTHOR]

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class A p , where class A p is invariant (or symmetric) under rotations. The well-known class of Janowski functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the (p , q) -variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter p is obviously unnecessary. [ABSTRACT FROM AUTHOR]

In analysis, the introduction of q-calculus has been a revelation. It has a deep impact on various concepts and applications of pure and applied sciences. In this article we investigate certain geometric properties relating to convolution of functions of a newly defined class of analytic functions. The important region of the lemniscate of Bernoulli is considered. Here we utilize concepts of q-calculus which enhances and generalizes the vitality of this research work. In the same context we study the Fekete–Szegö problem. [ABSTRACT FROM AUTHOR]