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Univalence conditions for an integral operator defined by a generalization of the Srivastava-Attiya operator

Srivastava H.M. (Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada + Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, Republic of China)
Juma Abdul Rahman S. (Department of Mathematics, University of Anbar, Ramadi, Iraq)
Zayed Hanaa M. (Department of Mathematics, Faculty of Science, Menofia University, Shebin Elkom , Egypt)

The main object of this paper is to introduce and study systematically the univalence criteria of a new family of integral operators by using a substantially general form of the widely-investigated Srivastava-Attiya operator. In particular, we derive several new sufficient conditions of univalence for this generalized Srivastava-Attiya operator. Relevant connections with other related earlier works are also pointed out.

Keywords: Analytic functions, Univalent functions, Hadamard product (or convolution), λ-Generalized Hurwitz-Lerch function, Series representations, Fox’s H-function, Mellin-Barnes contour integral, Integral operators, Srivastava-Attiya Operator