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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Study certain subclasses of holomorphic functions for quasi-subordination

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pp. 865–871Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-2015XML
Received:
08 Oct 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2015
Pages:
865–871

Abstract

 Numerous scholars have shown remarkable interest in geometric function theory, a thriving area of study with roots in complex analysis. The investigation of the geometric properties of analytic (in addition to univalent) functions, with numerous applications in numerous branches of mathematics, mathematical physics, and engineering, is largely responsible for this. Applications in engineering designs, fluid flows in physics, special functions, orthogonal polynomials, and conformal mappings are noteworthy. The article investigates a subclass of quasi-subordination-related analytic and univalent functions established in the domain of logistics sigmoid functions on a unit disk. Using quasi-subordination, the Fekete-Szego functional  |e3 – μe22| can be obtained for functions of the classes  Sq* (τ, γ, ℧),  and Gq (ϑ, α, ℧). We also briefly discuss the subordination results and the improved results for the related classes involving majorization. Some renowned subclasses of analytic and univalent functions, including the classes of starlike functions and convex functions, are included in the definition of the novel class. The description of the class involves the application of two fundamental mathematical concepts: quasi-subordination and Taylor’s series.

Keywords

Subject Classifications

30C45

References

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