Abstract

This paper introduces a novel computational strategy devised to address the challenges encountered in approximation theory. The strategy revolves around the utilization of extended pseudo-Chebyshev wavelet approximations, a concept pioneered by Lal et al. in 2022, which is grounded in the method of pseudo-Chebyshev wavelets approximation. The paper meticulously delineates the methodology, along with an evaluation of error for a specific function. To showcase the efficacy and efficiency of the extended pseudo-Chebyshev wavelet approximation approach, significant discoveries are exemplified through a practical instance. Furthermore, the paper establishes the error of a function associated with the class of absolutely continuous functions using extended pseudo-Chebyshev wavelets via orthogonal projection operators, thereby affirming these estimators as notably more precise and theoretically optimal within the domain of wavelet analysis.

Keywords and Phrases

Absolute Continuity, Wavelets, Extended pseudo Chebyshev wavelets, Orthogonal projection operators.

A.M.S. subject classification

40A30, 42C15, 42A16, 42C40, 65T60, 65L10, 65L60, 65R20.

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