Fekete--Szeg\H{o} Inequalities for New Subclasses of Bi-Univalent Functions Defined by S\u{a}l\u{a}gean $q$-Differential Operator

Authors

  • Mohammad Al-Ityan Department of Mathematics, Faculty of Science, Al-Balqa Applied University, 19117, Salt, Jordan
  • Ala Amourah Department of Mathematics, Faculty of Education and Arts, Sohar University, Sohar 3111, Sultanate of Oman,
  • Abdullah Alsoboh Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman
  • Nidal Anakira Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman.
  • Mohammad Bani Raba’a Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, Jordan
  • Suha Hammad Department of Mathematics, College of Education for Pure Sciences University of Tikrit, Iraq
  • Tala Sasa Department of Mathematics, Faculty of Science, Applied Science Private University, Amman, Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6115

Keywords:

Analytic Functions, $q$-S\u{a}l\u{a}gean Operator, Starlike Functions, Taylor Coefficients

Abstract

In this paper, we introduce a new operator based on the S\u{a}l\u{a}gean \( q \)-differential approach to define a new class of analytic functions. Using this operator, we obtain estimates for the first two coefficients in the Taylor series, \( |a_2| \) and \( |a_3| \). A significant part of the study focuses on the Fekete--Szeg\H{o} inequalities for the function classes \( \mathcal{M}_{\sigma,q,\Sigma}^{\zeta,m}(\leftthreetimes, \kappa, \alpha) \) and \( \mathcal{M}_{\sigma,q,\Sigma}^{\zeta,m}(\gamma,\leftthreetimes, \kappa) \). Through our analysis, we derive several important results, including some special cases that we present in this paper as Corollaries.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Complex Analysis

License

Copyright (c) 2025 Mohammad Al-Ityan, Ala Amourah, Abdullah Alsoboh, Nidal Anakira, Mohammad Bani Raba’a , Suha Hammad, Tala Sasa

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How to Cite

Fekete--Szeg\H{o} Inequalities for New Subclasses of Bi-Univalent Functions Defined by S\u{a}l\u{a}gean $q$-Differential Operator. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6115. https://doi.org/10.29020/nybg.ejpam.v18i2.6115