Certain Quantum Operator Related to Generalized Mittag–Leffler Function

Mansour F. Yassen () and Adel A. Attiya
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Mansour F. Yassen: Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia
Adel A. Attiya: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 24, 1-15

Abstract: In this paper, we present a novel class of analytic functions in the form h ( z ) = z p + ∑ k = p + 1 ∞ a k z k in the unit disk. These functions establish a connection between the extended Mittag–Leffler function and the quantum operator presented in this paper, which is denoted by ℵ q , p n ( L , a , b ) and is also an extension of the Raina function that combines with the Jackson derivative. Through the application of differential subordination methods, essential properties like bounds of coefficients and the Fekete–Szegő problem for this class are derived. Additionally, some results of special cases to this study that were previously studied were also highlighted.

Keywords: Mittag–Leffler function; quantum calculus; Jackson differential operator; q -differentiation; q -integration; subordination relation; differential subordination; Fekete–Szeg? function; operators in geometric function theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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