Symmetry and Quantum Calculus in Defining New Classes of Analytic Functions

Fuad Alsarari, Abdulbasit Darem, Muflih Alhazmi () and Alaa Awad Alzulaibani
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Fuad Alsarari: Department of Mathematics and Statistics, College of Sciences in Yanbu, Taibah University, Madinah 46423, Saudi Arabia
Abdulbasit Darem: Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
Muflih Alhazmi: Mathematics Department, College of Science, Northern Border University, Arar 73213, Saudi Arabia
Alaa Awad Alzulaibani: Department of Mathematics and Statistics, College of Sciences in Yanbu, Taibah University, Madinah 46423, Saudi Arabia

Mathematics, 2025, vol. 13, issue 14, 1-12

Abstract: This paper introduces a novel class of analytic functions that integrates q -calculus, Janowski-type functions, and ( a , b )-symmetrical functions. By exploring convolution operations and quantum calculus, we establish essential convolution conditions that lay the groundwork for subsequent research. Building on a new conceptual framework, we also define analogous neighborhoods for the classes F ¯ q a , b ( F , H ) and investigate related neighborhood properties. These developments provide a deeper understanding of the structural and analytical behavior of these functions, opening up avenues for future study.

Keywords: ( a , b )-symmetrical functions; analytic functions; convolution; starlike functions; q -calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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