The pseudo-Chebyshev wavelets and its applications in the error of the functions of bounded variation

This paper presents a novel computational approach to tackle challenges in approximation theory. The proposed method leverages pseudo-Chebyshev wavelet approximations, a concept introduced by Lal et al. in 2022, based on pseudo-Chebyshev functions. The paper provides a detailed description of the method, followed by an error analysis for a given function. Key results are illustrated through an example, highlighting the accuracy and efficiency of the pseudo-Chebyshev wavelet approximation technique. Fur-thermore, the paper derives error estimates for functions of bounded variation using pseudo-Chebyshev wavelets via orthogonal projection operators, demonstrating that these estimators are exceptionally precise and optimal in the context of wavelet analysis.