Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function

Tayyah, Adel Salim; Yalçın, Sibel; Bayram, Hasan

doi:10.3390/math13233878

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Open AccessArticle

Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function

by

Adel Salim Tayyah

^1,†

,

Sibel Yalçın

^2,*,†

and

Hasan Bayram

^2,†

¹

Department of Cybersecurity, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq

²

Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludağ University, 16059 Bursa, Türkiye

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2025, 13(23), 3878; https://doi.org/10.3390/math13233878

Submission received: 10 November 2025 / Revised: 28 November 2025 / Accepted: 2 December 2025 / Published: 3 December 2025

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

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Abstract

In this paper, we introduce a new class of analytic functions, denoted by

S (ν, φ_{ϑ, e})

, and provide illustrative examples to elucidate its properties. This class generalizes the starlike and convex functions previously defined by Khatter et al. in relation to the exponential function. A significant contribution of this work is the derivation of sharp bounds for various coefficient-related problems within this class. The computational challenges involved in deriving these bounds were effectively addressed using Mathematica

^{TM}

codes. Additionally, figures illustrating the geometric properties and essential computations have been incorporated into the paper.

Keywords: analytic functions; starlike and convex functions; exponential function; coefficient bounds; subordination; Hankel determinants

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MDPI and ACS Style

Tayyah, A.S.; Yalçın, S.; Bayram, H. Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function. Mathematics 2025, 13, 3878. https://doi.org/10.3390/math13233878

AMA Style

Tayyah AS, Yalçın S, Bayram H. Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function. Mathematics. 2025; 13(23):3878. https://doi.org/10.3390/math13233878

Chicago/Turabian Style

Tayyah, Adel Salim, Sibel Yalçın, and Hasan Bayram. 2025. "Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function" Mathematics 13, no. 23: 3878. https://doi.org/10.3390/math13233878

APA Style

Tayyah, A. S., Yalçın, S., & Bayram, H. (2025). Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function. Mathematics, 13(23), 3878. https://doi.org/10.3390/math13233878

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Sharp Coefficient Bounds for a Class of Analytic Functions Related to Exponential Function

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