Differential Subordination Results for Certain Integrodifferential Operator and Its Applications

Abstract

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