On Generalizations of the Close-to-Convex Functions Associated with q -Srivastava–Attiya Operator

Daniel Breaz, Abdullah A. Alahmari, Luminiţa-Ioana Cotîrlă () and Shujaat Ali Shah
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Daniel Breaz: Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Abdullah A. Alahmari: Department of Mathematical Sciences, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Luminiţa-Ioana Cotîrlă: Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Shujaat Ali Shah: Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology (QUEST), Nawabshah 67450, Pakistan

Mathematics, 2023, vol. 11, issue 9, 1-10

Abstract: The study of the q -analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the q -difference operator. Moreover, by using the q -analogues of a certain family of linear operators, the classes K q , b s h , K ˜ q , s b h , Q q , b s h , and Q ˜ q , s b h are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the q -Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration.

Keywords: analytic functions; q -starlike functions; q -convex functions; q -close-to-convex functions; q -Srivastava–Attiya operator; q -multiplier transformation (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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