Differential subordination results for certain integrodifferential operator and its applications. (English) Zbl 1256.30008
Summary: We introduce an integrodifferential operator \(J_{s,b}(f)\) which plays an important role in geometric function theory. Some theorems in differential subordination for \(J_{s,b}(f)\) are used. Applications to analytic number theory are also obtained which give new results for the Hurwitz-Lerch zeta function and the polylogarithmic function.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
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