| Issue |
Math. Model. Nat. Phenom.
Volume 12, Number 3, 2017
Special functions and analysis of PDEs
|
|
|---|---|---|
| Page(s) | 65 - 71 | |
| DOI | https://doi.org/10.1051/mmnp/201712306 | |
| Published online | 31 May 2017 | |
Some Comprehensive Inequalities Consisting of Mittag-Leffler Type Functions in the Complex Plane
1
Department of Mathematics, Faculty of Science, Çankiri Karatekin University Uluyazi Campus, 18100 Çanikri, Turkey
2
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
* Corresponding author. E-mail: goyal.praveen2011@gmail.com
Inequalities involving Mittag-Leffler functions play important rôles in themselves and in their diverse applications. Many inequalities involving Mittag-Leffler functions have been established by a number of authors in many different ways. In this paper by making use of a novel idea and technique, a comprehensive result which contains several differential inequalities (in the complex plane ℂ) relating to the Mittag-Leffler (type) functions:
(in its kernel (λ)v being the familier Pochhammer symbol) is first established. A number of corollaries and consequences of the main result are then presented.
Mathematics Subject Classification: 30A10 / 33E12 / 26D07
Key words: complex plane / unit open disk / Jack's lemma / analytic functions / differential inequalities in the complex plane / Mittag-Leffler (type) functions / complex special functions
© EDP Sciences, 2017
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