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

By Bilal Khan, Hari M. Srivastava, Muhammad Tahir, Maslina Darus, Qazi Zahoor Ahmad, Nazar Khan. AIMS Mathematics, 2021

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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.

Subfields: Geometry and Topology, Pharmacology

View Paper: https://www.semanticscholar.org/paper/e1329ca3618da33caad1717cb07800f399aa9569