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Zbl 1112.30007
Srivastava, H.M.; Attiya, A.A.
An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination. (English)
[J] Integral Transforms Spec. Funct. 18, No. 3, 207 - 216 (2007). ISSN 1065-2469; ISSN 1476-8291/e

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.

MSC 2000:: *30C10 Polynomials (one complex variable)
30C45 Special classes of univalent and multivalent functions
11M35 Other zeta functions

Keywords: analytic functions; univalent functions; convex functions; starlike functions; differential subordination; Hurwitz-Lerch zeta function; Riemann and Hurwitz (or generalized) zeta functions; polylogarithmic function; Jung-Kim-Srivastava integral operator; Hadamard product (or convolution); mutiplier transformations; Koebe function of order $\alpha$

Cited in: Zbl 1195.30029 Zbl 1130.30003

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