Symmetry and Quantum Calculus in Defining New Classes of Analytic Functions - Fuad Alsarari; Abdulbasit Darem; Muflih Alhazmi; Alaa Awad Alzulaibani (Mathematics)
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 <semantics><msubsup><mover>F¯</mover>qa,b</msubsup>(F,H)</semantics> 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.