This article is cited in 4 papers

A class of bi-Bazilevic̆ and bi-pseudo-starlike functions involving tremblay fractional derivative operator

A. S. Tayyah, W. G. Atshan

Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah 58002, Iraq

Abstract: In this paper, we introduce a new class of bi-univalent functions, which exhibit connections to Bazilevic̆ and Pseudo-Starlike functions. By employing the Tremblay fractional derivative operator, we establish this comprehensive class. For functions within this class, we derive coefficient inequalities and the Fekete-Szegö inequalities. Furthermore, we discuss various significant observations related to the presented results. Additionally, we provide some non-trivial examples within this class, supplemented by illustrative figures to enhance understanding.

Keywords: pseudo-starlike function, Bazilevic̆ function, bi-univalent functions, fractional derivative, Fekete-Szegö inequality.

UDC: 517.54

MSC: Primary 30C45; Secondary 30C50

Received: 25.09.2024
Revised: 11.01.2025
Accepted: 12.01.2025

Language: English

DOI: 10.15393/j3.art.2025.16750