Applications of a certain q-integral operator to the subclasses of analytic and bi-univalent functions

Abstract

In the present investigation, our aim is to define a generalized subclass of analytic and bi-univalent functions associated with a certain $q$-integral operator in the open unit disk $\mathbb{U}$. We estimate bounds on the initial Taylor-Maclaurin coefficients $\left \vert a_{2}\right \vert$ and $\left \vert a_{3}\right \vert $ for normalized analytic functions $f$ in the open unit disk by considering the function $f$ and its inverse $g = f^{{-}{1}}$. Furthermore, we derive special consequences of the results presented here, which would apply to several (known or new) subclasses of analytic and bi-univalent functions.

Keywords

• analytic functions
• univalent functions
• taylor-maclaurin series expansions
• taylor-maclaurin initial coefficients
• bi-univalent functions
• q-derivative (or q-difference) operator
• q-integral operator