Bernoulli polynomials for a new subclass of Te-univalent functions

G Saravanan; S Baskaran; B Vanithakumari; Lulah Alnaji; Timilehin Gideon Shaba; Isra Al-Shbeil; Alina Alp Lupas

doi:10.1016/j.heliyon.2024.e33953

Bernoulli polynomials for a new subclass of Te-univalent functions

Heliyon. 2024 Jul 9;10(14):e33953. doi: 10.1016/j.heliyon.2024.e33953. eCollection 2024 Jul 30.

Authors

G Saravanan¹, S Baskaran², B Vanithakumari^{3

2}, Lulah Alnaji⁴, Timilehin Gideon Shaba⁵, Isra Al-Shbeil¹, Alina Alp Lupas⁶

Affiliations

¹ Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan.
² Department of Mathematics, Agurchand Manmull Jain College, Meenambakkam, Chennai, 600061, Tamilnadu, India.
³ Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Chennai, 601103, Tamilnadu, India.
⁴ Department of Mathematics, College of Science, University of Hafr Al-Batin, Hafr Al-Batin, 39524, Saudi Arabia.
⁵ Department of Physical Sciences, Mathematics Programme, Landmark University, Omu-Aran 251103, Nigeria.
⁶ Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania.

Abstract

This paper introduces a novel subclass, denoted as $T_{σ}^{q, s} (μ_{1}; ν_{1}, κ, x)$ , of Te-univalent functions utilizing Bernoulli polynomials. The study investigates this subclass, establishing initial coefficient bounds for $| a_{2} |$ , $| a_{3} |$ , and the Fekete-Szegö inequality, namely $| a_{3} - ζ a_{2}^{2} |$ , are derived for this class. Additionally, several corollaries are provided to further elucidate the implications of the findings.

Keywords: Analytic functions; Bernoulli polynomials; Fekete-Szegö problem; Te-univalent functions; Univalent functions; primary, 30C45, 30C15.