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Applications of q‐Derivative Operator to the Subclass of Bi‐Univalent Functions Involving q‐Chebyshev Polynomials

Author

Listed:
  • Bilal Khan
  • Zhi-Guo Liu
  • Timilehin Gideon Shaba
  • Serkan Araci
  • Nazar Khan
  • Muhammad Ghaffar Khan

Abstract

In recent years, the usage of the q‐derivative and symmetric q‐derivative operators is significant. In this study, firstly, many known concepts of the q‐derivative operator are highlighted and given. We then use the symmetric q‐derivative operator and certain q‐Chebyshev polynomials to define a new subclass of analytic and bi‐univalent functions. For this newly defined functions’ classes, a number of coefficient bounds, along with the Fekete–Szegö inequalities, are also given. To validate our results, we give some known consequences in form of remarks.

Suggested Citation

  • Bilal Khan & Zhi-Guo Liu & Timilehin Gideon Shaba & Serkan Araci & Nazar Khan & Muhammad Ghaffar Khan, 2022. "Applications of q‐Derivative Operator to the Subclass of Bi‐Univalent Functions Involving q‐Chebyshev Polynomials," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8162182
    DOI: 10.1155/2022/8162182
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    References listed on IDEAS

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    1. Saeed Islam & Muhammad Ghaffar Khan & Bakhtiar Ahmad & Muhammad Arif & Ronnason Chinram, 2020. "Q -Extension of Starlike Functions Subordinated with a Trigonometric Sine Function," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
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    Cited by:

    1. Mohammad Faisal Khan & Nazar Khan & Serkan Araci & Shahid Khan & Bilal Khan, 2022. "Coefficient Inequalities for a Subclass of Symmetric q ‐Starlike Functions Involving Certain Conic Domains," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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