Applications of Some Subclasses of Meromorphic Functions Associated with the q -Derivatives of the q -Binomials

Ekram E. Ali, Hari M. Srivastava (), Abdel Moneim Y. Lashin and Abeer M. Albalahi
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Ekram E. Ali: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Abdel Moneim Y. Lashin: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abeer M. Albalahi: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia

Mathematics, 2023, vol. 11, issue 11, 1-10

Abstract: In this article, we make use of the q -binomial theorem to introduce and study two new subclasses ℵ ( α q , q ) and ℵ ( α , q ) of meromorphic functions in the open unit disk U , that is, analytic functions in the punctured unit disk U ∗ = U \ { 0 } = { z : z ∈ C and 0 < z < 1 } . We derive inclusion relations and investigate an integral operator that preserves functions which belong to these function classes. In addition, we establish a strict inequality involving a certain linear convolution operator which we introduce in this article. Several special cases and corollaries of our main results are also considered.

Keywords: q-derivatives of binomials; Jackson’s q-integrals; analytic functions; starlike and convex functions; analytic and meromorphic functions; hadamard product (or convolution); q-Bernardi integral operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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