Two dimensional pseudo-Chebyshev wavelets and their application in the theory of approximation of functions belonging to Hölders class

Abstract

For the first time in 2022, the authors introduced the notion of pseudo-Chebyshev wavelets in the context of one dimension. Continuing the study in advance sense, in this article, two dimensional pseudo Chebyshev wavelets are introduced. Two dimensional pseudo Chebyshev wavelet expansion of a function of two variable is defined and verified. This research paper introduces a novel algorithm based on the two dimensional pseudo Chebyshev wavelet method to address computation problems in approximation theory. The methods are illustrated by an example and compared with prominent Chebyshev wavelet methods to demonstrate the validity and applicability of the results. The error analysis and convergence analysis of a functions in the Hölder classes have been studied by this wavelets. More over the error of approximation of functions of Holder’s class have been estimated by an orthogonal projection operators of its two dimensional pseudo Chebyshev wavelets. The results of this paper are the significant developments in wavelet analysis. © 2020 Mathematics Subject Classification.