Mapping properties of holomorphic function associated with Gaussian hypergeometric function

Abstract

This paper aims to present the associated results of holomorphic function J(z) := Jµ,δ(p, q; r; z) defined on open unit disc U = {z ∈ C : |z| < 1}, belongs to ϕ* (A, B) and K(A, B). This work also consider an integral operator I(z) associated with the hypergeometric functions and identified the necessary and sufficient condition for I(z) belongs to ϕ* (A, B) as well as K(A, B).