The order of close-to-convexity and integral operators of analytic functions of complex order

Sabri, Mustafa A.

doi:10.47974/JIM-2298

Open Access Research Article

The order of close-to-convexity and integral operators of analytic functions of complex order

^*Mustafa A. SabriCorresponding authormustafasabri.edbs@uomustansiriyah.edu.iqDepartment of MathematicsCollege of EducationMustansiriyah UniversityBaghdad, IraqView full profile →

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pp. 1173–1178Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2298XML

Received:: 01 May 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2298
Pages:: 1173–1178

Abstract

This paper investigates the orders of close-to-convexity for analytic functions of complex order defined in the open unit disc. Sufficient conditions are established under which certain integral operators transform analytic functions into the class κ(γ,δ), representing a generalized form of the classical close-to-convex function class. Several new extensions of previously established results are obtained, together with sharp bounds for the related differential inequalities. The study further enhances the understanding of the geometric behavior of analytic functions under the action of complex-order integral operators.

Keywords

Convex Integrals operator Analytic function Complex orders

Subject Classifications

30C45

References

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