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Studying the Harmonic Functions Associated with Quantum Calculus

Author

Listed:
  • Abdullah Alsoboh

    (Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia)

  • Ala Amourah

    (Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan)

  • Maslina Darus

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Carla Amoi Rudder

    (Faculty of Resilience, Rabdan Academy, Abu Dhabi P.O. Box 114646, United Arab Emirates)

Abstract

Using the derivative operators’ q -analogs values, a wide variety of holomorphic function subclasses, q -starlike, and q -convex functions have been researched and examined. With the aid of fundamental ideas from the theory of q -calculus operators, we describe new q -operators of harmonic function H ϱ , χ ; q γ F ( ϖ ) in this work. We also define a new harmonic function subclass related to the Janowski and q -analog of Le Roy-type functions Mittag–Leffler functions. Several important properties are assigned to the new class, including necessary and sufficient conditions, the covering Theorem, extreme points, distortion bounds, convolution, and convex combinations. Furthermore, we emphasize several established remarks for confirming our primary findings presented in this study, as well as some applications of this study in the form of specific outcomes and corollaries.

Suggested Citation

  • Abdullah Alsoboh & Ala Amourah & Maslina Darus & Carla Amoi Rudder, 2023. "Studying the Harmonic Functions Associated with Quantum Calculus," Mathematics, MDPI, vol. 11(10), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2220-:d:1142258
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    References listed on IDEAS

    as
    1. Georgia Irina Oros, 2020. "Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions," Mathematics, MDPI, vol. 8(11), pages 1-8, November.
    2. Alina Alb Lupaş & Georgia Irina Oros, 2022. "Fuzzy Differential Subordination and Superordination Results Involving the q -Hypergeometric Function and Fractional Calculus Aspects," Mathematics, MDPI, vol. 10(21), pages 1-11, November.
    3. Abdullah Alsoboh & Ala Amourah & Maslina Darus & Rami Issa Al Sharefeen, 2023. "Applications of Neutrosophic q -Poisson distribution Series for Subclass of Analytic Functions and Bi-Univalent Functions," Mathematics, MDPI, vol. 11(4), pages 1-10, February.
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    Citations

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    Cited by:

    1. Abdullah Alsoboh & Georgia Irina Oros, 2024. "A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q ̧ -Calculus," Mathematics, MDPI, vol. 12(10), pages 1-15, May.
    2. Ala Amourah & Abdullah Alsoboh & Daniel Breaz & Sheza M. El-Deeb, 2024. "A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via q ̧ -Calculus," Mathematics, MDPI, vol. 12(11), pages 1-13, June.

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