Properties for Close-to-Convex and Quasi-Convex Functions Using q -Linear Operator

Ekram E. Ali, Rabha M. El-Ashwah (), Abeer M. Albalahi and Wael W. Mohammed
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Ekram E. Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Rabha M. El-Ashwah: 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 2440, Saudi Arabia
Wael W. Mohammed: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

Mathematics, 2025, vol. 13, issue 6, 1-10

Abstract: In this work, we describe the q -analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators I q , ρ s ( ν , τ ) , and we obtain findings related to geometric function theory (GFT) by utilizing approaches established through subordination and knowledge of q -calculus operators. By using this operator, we develop generalized classes of quasi-convex and close-to-convex functions in this paper. Additionally, the classes K q , ρ s ( ν , τ ) φ , Q q , ρ s ( ν , τ ) φ are introduced. The invariance of these recently formed classes under the q -Bernardi integral operator is investigated, along with a number of intriguing inclusion relationships between them. Additionally, several unique situations and the beneficial outcomes of these studies are taken into account.

Keywords: analytic function; q-starlike functions; q-convex functions; q-close-to-convex functions; q-analogue Catas operator; q-analogue of Ruscheweyh operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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