Wavelet‐Infused q ‐Szász‐Kantorovich Operators for Lp‐Approximation: Theory and Applications

ABSTRACT

The primary objective of this research is to establish and analyze wavelet‐type approximation properties for a newly constructed class of ‐Szász‐Kantorovich operators. This work bridges quantum calculus (‐calculus) and wavelet analysis to enhance function approximation in various mathematical spaces. Furthermore, the results demonstrate that these operators are a general extension of several classical frameworks, including the ‐Szász‐Mirakjan and standard Kantorovich operators. We explore wavelet‐type approximation properties for ‐Szász‐Kantorovich operators by introducing specific unbounded positive sequences. Our construction integrates ‐Szász type operators with wavelet‐based Kantorovich variants to achieve ‐approximation results for . Furthermore, we use the Ditzian‐Totik ‐functional to characterize second‐order Lipschitz spaces and establish fundamental inequalities. Moreover, the numerical illustrations demonstrate that this wavelet‐infused approach is particularly favorable for approximating functions that exhibit both smoothness and rapid growth.