Geometric Properties of Generalized Janowski Type Functions

Authors

Muflih Alhazmi Mathematics Department, Faculty of Science, Northern Border University, Arar, KSA, Saudi Arabia https://orcid.org/0000-0001-8758-1781
Al-Rezami A. Y Mathematics Department, Prince Sattam Bin Abdulaziz University, Al-Kharj, 16278, Saudi Arabia
Erhan D Department of Mathematics, Faculty of Science and Letters, Kafkas University, Campus, 36100, Kars, Türkiye https://orcid.org/0009-0009-6315-7885
Abdulbasit A. Darem Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, 73213, Saudi Arabia https://orcid.org/0000-0002-5650-1838
Fuad Alsarari Department of Mathematics and statistics, College of Sciences, Yanbu, Taibah University, Saudi Arabia https://orcid.org/0000-0002-4759-5449

DOI:

https://doi.org/10.37256/cm.6520255736

Keywords:

subordination, convolution conditions, starlike functions, convex functions, Janowski type functions

Abstract

The present paper aims to explore subclasses of analytic functions that extend the class of Janowski-type functions. We examine specific convolution conditions that ensure functions h fall within the generalized Janowski-type classes of starlike and convex functions. These conditions will serve as foundational results for further analysis in this study. Additionally, we provide sufficient conditions and neighborhood results pertinent to functions within the starlike class. Finally, we investigate the invariance properties of the operator h_μ(ϑ) = (1 − μ)ϑ + μh(ϑ), 0 < μ < 1, as it applies to functions in this classification.

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Published

2025-09-23

Issue

Contemporary Mathematics, Volume 6 Issue 5 (2025)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.