Applications of \(q\)-Mittag-Leffler type Poisson distribution to subclass of \(q\)-starlike functions

Volume 29, Issue 3, pp 272--282 https://doi.org/10.22436/jmcs.029.03.06

Publication Date: November 01, 2022 Submission Date: July 20, 2022 Revision Date: August 05, 2022 Accteptance Date: August 18, 2022

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Authors

Sh. Aziz - Government Post Graduate Collage Dargai, Pakistan. Kh. Ahmad - Government Post Graduate Collage Dargai, Pakistan. B. Khan - School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, Peoples Republic of China. Z. Salleh - Department of Mathematics, Feculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Kaula Nerus, 21030, Terengganu, Malaysia. Sh. Ali - Government Post Graduate Collage Dargai, Pakistan. H. Bilal - Government Post Graduate Collage Dargai, Pakistan. M. Gh. Khan - Institute of Numerical Sciencies, Kohat University of Science and Technology, Kohat, Pakistan.

Abstract

In the recent years, the usage of special functions in combinations with the \(q\) -series has got attraction of a number of mathematicians. In this paper, we first highlighted and studied some well-known celebrated special functions. We then use the idea of convolution and define a new series, namely the series of \(q\)-Mittag-Leffler functions with the \(q\)-Poisson distribution. Finally by using the \(q\)-Mittag-Leffler type \(q\)-Poisson distribution we then define a new subclass of \(q\)-Starlike functions associated with the Janwoski functions. We derive a number of useful results like the Fekete-Szego problems, distortion theorems and a sufficient condition.

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Keywords

• Analytic functions
• starlike function
• Mitag-Leffer and \(q\)-Mittag-Leffler functions
• \(q\)-Poisson distribution
• Janowski function

MSC

•  30C45
•  30D30

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