On Coefficient Inequalities of Certain Subclasses of Bi-Univalent Functions Defined Using q-Differential Operator Involving q-Poisson Distribution
Ranjan S. Khatu *
Department of Mathematics, Shriram Kusumtai Sadashiv Vanjare College, Lanja-416701, India.
Santosh D. Jadhav
Department of Mathematics, Sandip University, Nashik, Maharashtra, India.
Renu P. Pathak
Department of Mathematics, Sandip University, Nashik, Maharashtra, India.
*Author to whom correspondence should be addressed.
Abstract
In this research paper, a new subclass of bi-univalent and analytic functions on unit disc \(\Delta\) = {z \(\in\) \(\mathbb{C}\) : |z| < 1} is defined. The zero-truncated Poisson distribution function and q-differential operator are used to define this subclass. Furthermore, we also establish the upper bounds on the second and third coefficients of functions in the same class.
Keywords: Analytic function, q- differential operator, Bi-univalent function, Taylor-Maclaurin series expansion, coefficient bounds, zero-truncated Poisson differential operator