MAPPING PROPERTIES OF HOLOMORPHIC FUNCTION ASSOCIATED WITH GAUSSIAN HYPERGEOMETRIC FUNCTION

MAPPING PROPERTIES OF HOLOMORPHIC FUNCTION ASSOCIATED WITH GAUSSIAN HYPERGEOMETRIC FUNCTION

P. Yadav, S. Joshi, H. Pawar

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Abstract

This paper aims to present the associated results of holomorphic function J(z) := J ; (p; q; r; z) de ned on open unit disc U = fz 2 C : jzj < 1g, belongs to ' (A;B) and K(A;B). This work also consider an integral operator I(z) associated with the hypergeometric functions and identi ed the necessary and su cient condition for I(z) belongs to ' (A;B) as well as K(A;B).

Keywords

holomorphic function, starlike function, convex function, hypergeometric function.