Study of quantum calculus for a new subclass of bi-univalent functions associated with the cardioid domain

Abstract

In this article, we make use of the concepts of subordination and the q-calculus theory to analyze a new class of analytic bi-univalent functions associated to the cardioid domain. Our main focus is to derive a sharp inequality for a newly defined class of analytic and bi-univalent functions in the open unit disc U. We explore the bounds of initial coefficients, Fekete-Szegö type problems, and coefficient inequalities for newly established families. In addition, we explore some recent findings for the bi-univalent function and inverse function. Additionally, a few well-known results are mentioned to help make links between earlier and current results.

Keywords

• Analytic functions
• Bi-univalent functions
• Quantum-calculus
• Shell-like curve
• Coefficients inequalities
• Cardioid domain