Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator

Yehia, Abdelrahman M.; Hashem, Atef F.; Madian, Samar M.; Tharwat, Mohammed M.

doi:10.3390/axioms14090684

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Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator

¹

Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62611, Egypt

²

Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia

³

Basic Science Department, Higher Institute of Engineering and Technology, New Damietta 34517, Egypt

^*

Author to whom correspondence should be addressed.

Axioms 2025, 14(9), 684; https://doi.org/10.3390/axioms14090684 (registering DOI)

Submission received: 18 July 2025 / Revised: 29 August 2025 / Accepted: 3 September 2025 / Published: 5 September 2025

(This article belongs to the Special Issue New Developments in Geometric Function Theory, 4th Edition)

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Abstract

In this paper, we present a new integral operator that acts on a class of meromorphic functions on the punctured unit disc

U^{*}

. This operator enables the definition of a new subclass of meromorphic univalent functions. We obtain sharp bounds for the Fekete–Szegö inequality and the second Hankel determinant for this class. The theoretical approach is based on differential subordination. Furthermore, we link these theoretical insights to applications in 2D electromagnetic field theory by outlining a physical framework in which the operator functions as a field transformation kernel. We show that the operator’s parameters correspond to physical analogs of field regularization and spectral redistribution, and we use subordination theory to simulate the design of vortex-free fields. The findings provide new insights into the interaction between geometric function theory and physical field modeling.

Keywords: meromorphic functions; Fekete–Szegö inequality; second Hankel determinant; electromagnetic field; subordination; effective potential; vortex-free flow

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MDPI and ACS Style

Yehia, A.M.; Hashem, A.F.; Madian, S.M.; Tharwat, M.M. Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator. Axioms 2025, 14, 684. https://doi.org/10.3390/axioms14090684

AMA Style

Yehia AM, Hashem AF, Madian SM, Tharwat MM. Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator. Axioms. 2025; 14(9):684. https://doi.org/10.3390/axioms14090684

Chicago/Turabian Style

Yehia, Abdelrahman M., Atef F. Hashem, Samar M. Madian, and Mohammed M. Tharwat. 2025. "Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator" Axioms 14, no. 9: 684. https://doi.org/10.3390/axioms14090684

APA Style

Yehia, A. M., Hashem, A. F., Madian, S. M., & Tharwat, M. M. (2025). Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator. Axioms, 14(9), 684. https://doi.org/10.3390/axioms14090684

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Sharp Bounds and Electromagnetic Field Applications for a Class of Meromorphic Functions Introduced by a New Operator

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