An integral operator associated with the Hurwitz–Lerch Zeta function and differential subordination

Abstract

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 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.

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 α

Acknowledgements

The present investigation was supported, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.