Classes of Ma-Minda type analytic functions associated with a kidney-shaped domain

Adel Salim Tayyah; Sarem H. Hadi; Zhi-Gang Wang; Alina Alb Lupaş; Adel Salim Tayyah; Sarem H. Hadi; Zhi-Gang Wang; Alina Alb Lupaş

doi:10.3934/math.20251000

AIMS Mathematics

2025, Volume 10, Issue 9: 22445-22470. doi: 10.3934/math.20251000

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Research article

Classes of Ma-Minda type analytic functions associated with a kidney-shaped domain

1.
Department of Computer Science, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq
2.
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
3.
Department of Business Management, Al-imam University College, Balad 34011, Iraq
4.
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, Hunan, China
5.
Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, Oradea 410087, Romania

Received: 11 July 2025 Revised: 02 September 2025 Accepted: 15 September 2025 Published: 28 September 2025
MSC : 05A30, 11B65, 30C45, 47B38

Ma-Minda-type analytic functions have been a central topic in geometric function theory due to their importance in studying properties such as univalence, convexity, and starlikeness. However, the class of Ma-Minda functions associated with kidney-shaped domains has not been systematically investigated before, leaving a clear research gap. In this paper, we introduced and studied the geometric properties of class $ {\mathcal{S}}^*_k $. Our approach combined rigorous geometric analysis with Python programming (version 3.13.2) and graphical illustrations, providing both theoretical depth and computational support. Several inclusion relations and radius problems for $ {\mathcal{S}}^*_k $ were established in comparison with other known classes. Furthermore, we examined various problems related to the initial coefficient bounds, with particular emphasis on their sharpness.
- starlike functions,
- subordination,
- radius problem,
- coefficient estimates,
- Hankel determinants
Citation: Adel Salim Tayyah, Sarem H. Hadi, Zhi-Gang Wang, Alina Alb Lupaş. Classes of Ma-Minda type analytic functions associated with a kidney-shaped domain[J]. AIMS Mathematics, 2025, 10(9): 22445-22470. doi: 10.3934/math.20251000

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Abstract

Ma-Minda-type analytic functions have been a central topic in geometric function theory due to their importance in studying properties such as univalence, convexity, and starlikeness. However, the class of Ma-Minda functions associated with kidney-shaped domains has not been systematically investigated before, leaving a clear research gap. In this paper, we introduced and studied the geometric properties of class $ {\mathcal{S}}^*_k $. Our approach combined rigorous geometric analysis with Python programming (version 3.13.2) and graphical illustrations, providing both theoretical depth and computational support. Several inclusion relations and radius problems for $ {\mathcal{S}}^*_k $ were established in comparison with other known classes. Furthermore, we examined various problems related to the initial coefficient bounds, with particular emphasis on their sharpness.

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