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

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-04, Vol.11 (9), p.2022
Main Authors: Daniel Breaz, Abdullah A. Alahmari, Luminiţa-Ioana Cotîrlă, Shujaat Ali Shah
Format: Article
Language:English
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Summary: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 ,bs h , K˜ q ,sb h , Q q ,bs h , and Q˜ q ,sb 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.
ISSN:2227-7390
DOI:10.3390/math11092022