An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination. (English) Zbl 1112.30007

Summary: The main object of this article is to introduce and investigate an integral operator \(J_{s, b}(f)\) defined, by using the Hurwitz-Lerch Zeta function, on the various subclasses of the class of normalized analytic functions \(f\) in the open unit disk \(\mathbb U\). Using the technique of differential subordination, an interesting property of the general integral operator \(J_{s, b}(f)\) is obtained. Some applications of the results presented here are also considered.


30C10 Polynomials and rational functions of one complex variable
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
11M35 Hurwitz and Lerch zeta functions
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