On subordination relations of analytic functions associated with linear operators

Adel A. Attiya; Nak Eun Cho; Mansour F. Yassen; Adel A. Attiya; Nak Eun Cho; Mansour F. Yassen

doi:10.3934/math.20261076

AIMS Mathematics

2026, Volume 11, Issue 8: 26823-26833. doi: 10.3934/math.20261076

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Research article

On subordination relations of analytic functions associated with linear operators

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3.
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
4.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Damietta, Egypt

Received: 30 May 2026 Revised: 28 July 2026 Accepted: 14 August 2026 Published: 26 August 2026
MSC : 30C80, 30C55

This paper investigates important subordination properties of $ \beta $-convex functions defined on the open unit disk, in relation to a family of linear operators. By exploring these subordination properties, we identify certain constraints of these functions. In addition, applications to integral operators are also considered. Overall, the study contributes to both the theory of $ \beta $-convex functions and the general field of operator theory.
- subordination relation,
- univalent function,
- convex functions,
- $ \beta $-convex functions,
- Hadamard product,
- subordination chain,
- integral operator
Citation: Adel A. Attiya, Nak Eun Cho, Mansour F. Yassen. On subordination relations of analytic functions associated with linear operators[J]. AIMS Mathematics, 2026, 11(8): 26823-26833. doi: 10.3934/math.20261076

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Abstract

This paper investigates important subordination properties of $ \beta $-convex functions defined on the open unit disk, in relation to a family of linear operators. By exploring these subordination properties, we identify certain constraints of these functions. In addition, applications to integral operators are also considered. Overall, the study contributes to both the theory of $ \beta $-convex functions and the general field of operator theory.

References

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