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Some applications of Mittag-Leffler function in the unit disk

Attiya Adel A. (University of Mansoura, Faculty of Science, Department of Mathematics, Mansoura, Egypt + University of Hail, College of Science, Department of Mathematics, Hail, Saudi Arabia)

In this paper we introduce an operator associated with generalized Mittag-Leffler function in the unit disk U = {z : |z| < 1}. By using this operator and the virtue of differential subordination, we obtain interesting results. Some applications of our results are also obtained.

Keywords: Analytic functions, Mitttag-Leffler function, differential subordination, starlike functions, operators in geometric function theory