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An application of differential subordinations to the class of certain analytic functions. (English) Zbl 1176.30053

Summary: For functions belonging to a general class \(\mathcal R_p(k,\alpha,\lambda)\) of analytic functions in the open unit disc \(\mathbb U=\{z:| z|<1\}\), which are investigated int this paper, some applications of differential subordination are obtained, which contain an interesting property of the Hurwitz-Lerch Zeta 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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