Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities

Differential inequalities imposed by the extended hypergeometric function

Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of out...

Univalence of Certain Linear Operators Defined by Hypergeometric Function

Certain Sufficiency Conditions on Gaussian Hypergeometric Functions

The author aims at finding certain conditions on a, b and c such that the normalized Gaussian hypergeometric function zF (a, b; c; z) given by F (a, b; c; z) = ∞ ∑ n=0 (a, n)(b, n) (c, n)(1, n) z, |z| < 1, is in certain subclasses of analytic functions. A particular operator acting on F (a, b; c; z) is also discussed.

Sufficient conditions for univalence and starlikeness

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

On Integral Operator Involving Generalized Hypergeometric Function

Due to rigorous work on integral operators and the hypergeomet-ric functions, we define here an integral operator involving generalized hypergeometric function. By means of this generalized function, we introduce new classes of analytic functions and study their properties. 1 Introduction and preliminaries. Let H be the class of functions analytic in U := {z ∈ C : |z| < 1} and A be the subclass...