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

Hanen Louati, Afrah Y. Al-Rezami (), Abdulbasit A. Darem and Fuad Alsarari
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Hanen Louati: Department of Mathematics, College of Science, Northeren Border University, Arar 73222, Saudi Arabia
Afrah Y. Al-Rezami: Mathematics Department, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia
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

Mathematics, 2024, vol. 12, issue 16, 1-11

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.

Keywords: convolution; Janowski functions; q -calculus; ( ? , ? )-symmetric points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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