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Defining and Analyzing New Classes Associated with ( λ , γ )-Symmetrical Functions and Quantum Calculus

Author

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  • Hanen Louati

    (Department of Mathematics, College of Science, Northeren Border University, Arar 73222, Saudi Arabia
    Laboratory of PDEs and Applications (LR03ES04), Faculty of Science of Tunis, University of Tunis El Manar, Tunis 1068, Tunisia)

  • Afrah Y. Al-Rezami

    (Mathematics Department, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia
    Department of Statistics and Information, Sana’a University, Sana’a 1247, Yemen)

  • Abdulbasit A. Darem

    (Department of Computer Science, College of Science, Northern Border University, Arar 73222, Saudi Arabia)

  • Fuad Alsarari

    (Department of Mathematics and Statistics, College of Sciences, Taibah University, Yanbu 46423, Saudi Arabia)

Abstract

In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of ( λ , γ ) -symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class S q λ , γ ( x , y , z ) . Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes.

Suggested Citation

  • Hanen Louati & Afrah Y. Al-Rezami & Abdulbasit A. Darem & Fuad Alsarari, 2024. "Defining and Analyzing New Classes Associated with ( λ , γ )-Symmetrical Functions and Quantum Calculus," Mathematics, MDPI, vol. 12(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2603-:d:1462023
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