Related papers: Univalent Functions involving Generalized Hypergeo…
In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients.…
Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a…
The purpose of the present paper is to find the necessary and sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations…
If $g$ is an analytic function in the unit disc $\D $ we consider the generalized Hilbert operator $\hg$ defined by {equation*}\label{H-g} \mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt. {equation*} We study these operators acting on classical…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
Several integrals involving powers and ordinary hypergeometric functions are rederived by means of a generalized hypergeometric function of two variables (Appell's function) recovering some well-known expressions as particular cases. Simple…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
A motivation comes from {\em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference…
The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this…
It is known that, generically, Taylor series of functions holomorphic in the unit disc turn out to be universal series outside of the unit disc and in particular on the unit circle. Due to classical and recent results on the boundary…
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…
We establish generic existence of Universal Taylor Series on products $\Omega = \prod \Omega_i$ of planar simply connected domains $\Omega_i$ where the universal approximation holds on products $K$ of planar compact sets with connected…
In this paper, we study subclass of analytic function with negative coefficient defined by integral operator in the unit disc $U = \left\{ {z \in C:\left| z \right| < 1} \right\}$. The results are included coefficient estimates, closure…
We describe a new approach to the notion of general hypergeometric functions
The aim of this note is to provide a new identity connected with the Gauss hypergeometric function. This is achieved using results of certain combinatorial identities and a hypergeometric function approach.
This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the…
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…