Operator (biology)

Pure mathematics

Analytic function

Mathematics

Unit disk

Evolutionary biology

Transcription factor

Biology

Gene

Unit (ring theory)

Mathematics education

Analytic continuation

Mathematical analysis

Function (biology)

Repressor

Univalent function

Chemistry

Inverse

Geometry

Biochemistry

AIMS Mathematics

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.

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