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Keywords = q-analogue Catas operator

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10 pages, 261 KB  
Article
Properties for Close-to-Convex and Quasi-Convex Functions Using q-Linear Operator
by Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi and Wael W. Mohammed
Mathematics 2025, 13(6), 900; https://doi.org/10.3390/math13060900 - 7 Mar 2025
Cited by 2 | Viewed by 1157
Abstract
In this work, we describe the q-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators Iq,ρs(ν,τ), and we obtain findings related to geometric function theory (GFT) by utilizing approaches [...] Read more.
In this work, we describe the q-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators Iq,ρs(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 Kq,ρs(ν,τ)φ, Qq,ρs(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. Full article
18 pages, 288 KB  
Article
Application of Fuzzy Subordinations and Superordinations for an Analytic Function Connected with q-Difference Operator
by Ekram E. Ali, Rabha M. El-Ashwah and Abeer M. Albalahi
Axioms 2025, 14(2), 138; https://doi.org/10.3390/axioms14020138 - 15 Feb 2025
Cited by 1 | Viewed by 1069
Abstract
This paper extends the idea of subordination from the theory of fuzzy sets to the geometry theory of analytic functions with a single complex variable. The purpose of this work is to define fuzzy subordination and illustrate its main characteristics. New fuzzy differential [...] Read more.
This paper extends the idea of subordination from the theory of fuzzy sets to the geometry theory of analytic functions with a single complex variable. The purpose of this work is to define fuzzy subordination and illustrate its main characteristics. New fuzzy differential subordinations will be introduced with the help of this effort. We define a linear operator Iq,ρs(ν,ς) using the concept of the q-calculus operators. New fuzzy differential subordinations are created by employing the previously described operator, functions from the new class, and well-known lemmas. Specific corollaries derived from the operator proved the many examples created for the fuzzy differential subordinations, as well as the theorems, and demonstrate how the new theoretical conclusions apply to the fuzzy differential superordinations provided in this research. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
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