Approximation and convergence analysis of blending-type q-Baskakov operators using wavelet transformations

Abstract

This paper introduces a new class of blending-type operators constructed by integrating the q-Baskakov operators with wavelet-based approximations. Utilising the Kantorovich modification, we define a family of operators that allows for effective control over approximation properties while enabling smooth blending through wavelet scaling functions. Our analysis focuses on the convergence behaviour of these operators in both Lp and C[0, 1] spaces, providing detailed error estimates and smoothness properties. We establish the modulus of continuity and convergence rates, highlighting the advantages of the blending-type approach in approximation theory. Numerical examples are provided to illustrate the practical application and accuracy of the proposed operators, particularly in signal and function approximation scenarios.