Partial sums of generalized <em>q</em>-Mittag-Leffler functions

Muhammad Sabil Ur Rehman; Qazi Zahoor Ahmad; Hari M. Srivastava; Bilal Khan; Nazar Khan; Muhammad Sabil Ur Rehman; Qazi Zahoor Ahmad; Hari M. Srivastava; Bilal Khan; Nazar Khan

doi:10.3934/math.2020028

AIMS Mathematics

2020, Volume 5, Issue 1: 408-420. doi: 10.3934/math.2020028

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Research article

Partial sums of generalized q-Mittag-Leffler functions

1.
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan
2.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
4.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
5.
School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, People’s Republic of China

Received: 04 October 2019 Accepted: 25 November 2019 Published: 02 December 2019
MSC : Primary 05A30, 30C45; Secondary 11B65, 47B38

In the present investigation, our main aim is to give lower bounds for the ratio of some normalized q-Mittag-Leffler function and their sequences of partial sums. We consider various corollaries and consequences of our main results.
- univalent functions,
- analytic functions,
- partial sums,
- q-derivative (or q-difference) operator,
- normalized q-Mittag-Leffler function
Citation: Muhammad Sabil Ur Rehman, Qazi Zahoor Ahmad, Hari M. Srivastava, Bilal Khan, Nazar Khan. Partial sums of generalized q-Mittag-Leffler functions[J]. AIMS Mathematics, 2020, 5(1): 408-420. doi: 10.3934/math.2020028

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Abstract

In the present investigation, our main aim is to give lower bounds for the ratio of some normalized q-Mittag-Leffler function and their sequences of partial sums. We consider various corollaries and consequences of our main results.

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