Research article

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

  • Received: 11 May 2020 Accepted: 14 October 2020 Published: 06 November 2020
  • MSC : Primary 05A30, 30C45; Secondary 11B65, 47B38

  • 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.

    Citation: Bilal Khan, H. M. Srivastava, Muhammad Tahir, Maslina Darus, Qazi Zahoor Ahmad, Nazar Khan. Applications of a certain $q$-integral operator to the subclasses of analytic and bi-univalent functions[J]. AIMS Mathematics, 2021, 6(1): 1024-1039. doi: 10.3934/math.2021061

    Related Papers:

  • 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.


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