Geometric Attributes of Analytic Functions Generated by Mittag-Leffler Function

Ekram E. Ali (), Rabha M. El-Ashwah, Wafaa Y. Kota and Abeer M. Albalahi
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Ekram E. Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Rabha M. El-Ashwah: Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Wafaa Y. Kota: Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Abeer M. Albalahi: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia

Mathematics, 2025, vol. 13, issue 20, 1-25

Abstract: This study examines the necessary requirements for some analytic function subclasses, especially those associated with the generalized Mittag-Leffler function, to be classified as univalent function subclasses that are determined by particular geometric constraints. The core methodology revolves around the application of the Hadamard (or convolution) product involving a normalized Mittag-Leffler function M κ , χ ( ζ ) , leading to the definition of a new linear operator S χ , ϑ κ ℏ ( ζ ) . We investigate inclusion results in the recently defined subclasses Ξ ˜ ( ϖ , ϱ ) , L ^ ( ϖ , ϱ ) , K ^ ( ϖ , ϱ ) and F ^ ( ϖ , ϱ ) , which generalize the classical classes of starlike, convex, and close-to-convex functions. This is achieved by utilizing recent developments in the theory of univalent functions. In addition, we examine the behavior of functions from the class R θ ( E , V ) under the action of the convolution operator W χ , ϑ κ h ( ζ ) , establishing sufficient criteria for the resulting images to lie within the subclasses of analytic function. Also, certain mapping properties related to these subclasses are analyzed. In addition, the geometric features of an integral operator connected to the Mittag-Leffler function are examined. A few particular cases of our main findings are also mentioned and examined and the paper ends with the conclusions regarding the obtained results.

Keywords: Mittag-Leffler function; analytic functions; integral operator; Hadamard product; convex functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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