Generalized convolution properties based on the modified Mittag-Leffler function

Date

2017

Authors

Srivastava, H.M.
Kiliçman, Adem
Abdulnaby, Zainab E.
Ibrahim, Rabha W.

Journal Title

Journal ISSN

Volume Title

Publisher

Journal of Nonlinear Sciences and Applications

Abstract

Studies of convolution play an important role in Geometric Function Theory (GFT). Such studies attracted a large number of researchers in recent years. By making use of the Hadamard product (or convolution), several new and interesting subclasses of analytic and univalent functions have been introduced and investigated in the direction of well-known concepts such as the subordination and superordination inequalities, integral mean and partial sums, and so on. In this article, we apply the Hadamard product (or convolution) by utilizing some special functions. Our contribution in this paper includes defining a new linear operator in the form of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright pΨq-function in the right-half of the open unit disk where where R(z)>0. We then show that the new linear convolution operator is bounded in some spaces. In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright p Ψ -notation is used in our results.

Description

Keywords

Fractional calculus, analytic functions, fractional calculus operator, univalent functions, convex functions, Mittag-Leffler function, Fox-Wright p Ψ q -function, weighted μ -Bloch space, weighted-log Bloch space

Citation

Srivastava, H. M.; Kiliçman, A.; Abdulnaby, Z. E.; & Ibrahim, R. W. (2017). Generalized convolution properties based on the modified Mittag-Leffler function. Journal of Nonlinear Sciences and Applications, 10(8), article 4284-4294. DOI: 10.22436/jnsa.010.08.23