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In this paper, we provide sufficient conditions for constructing univalent analytic functions in the unit disk |z| < 1. We motivate our results through several examples and compare with the previously known coefficient conditions. Finally as an application, we present an interesting theorem involving Gaussian hypergeometric function. [ABSTRACT FROM AUTHOR]

In this paper, the generalized polylogarithm Φp, q(a, b, z), which is a particular representation of generalized hypergeometric functions, is considered. Conditions on the parameters a, b, p and q are found such that the normalized form of these generalized polylogarithms has certain geometric properties such as close-to-convexity, starlikeness and convexity in the open unit disc . Results for the Alexander transform of these generalized polylogarithm are also obtained. [ABSTRACT FROM AUTHOR]

The authors define a new subclass of A of functions involving complex order in the open unit disk U. For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce a generalized hypergeometric distribution and obtain some necessary and sufficient conditions for generalized hypergeometric distribution series belonging to certain classes of univalent functions associated with the conic domains. We also investigate some inclusion relations. Finally, we discuss an integral operator related to this series. [ABSTRACT FROM AUTHOR]