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Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions. (English) Zbl 1160.30325

Summary: The Srivastava-Attiya operator is used to define some new subclasses of strongly starlike and strongly convex functions of order \(\beta\) and type \(\alpha\) in the open unit disk \(\mathbb U\). For each of these new function classes, several inclusion relationships are established. Some interesting corollaries and applications of the results presented here are also discussed.

MSC:

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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