Differential Subordination Results for Certain Integrodifferential Operator and Its Applications

Abstract

We introduce an integrodifferential operator Js,b(f) which plays an important role in the Geometric Function Theory. Some theorems in differential subordination for Js,b(f) are used. Applications in Analytic Number Theory are also obtained which give new results for Hurwitz-Lerch Zeta function and Polylogarithmic function.