Convexity of Certain q-Integral Operators of p-Valent Functions

Abstract

By applying the concept (and theory) of fractional $q$-calculus, we first define and introduce two new $q$-integral operators for certain analytic functions defined in the unit disc $𝒰$. Convexity properties of these $q$-integral operators on some classes of analytic functions defined by a linear multiplier fractional $q$-differintegral operator are studied. Special cases of the main results are also mentioned.