Approximation by Haar polynomials in variable exponent grand Lebesgue spaces

AbstractIn this paper, we give direct theorems on approximation by Haar and Walsh polynomials in variable exponent grand Lebesgue space. Also the degree of approximation by Borel, Abel-Poisson, Riesz-Zygmund and Euler linear means of Haar-Fourier series are treated in the above-cited space.Keywords: Haar systemvariable exponent grand Lebesgue spacedirect approximation theoremlinear means of Haar–Fourier seriesMathematics Subject Classification (2010): 42C1046E30 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe work of author is supported by Program of Development of Regional Scientific and Educational Mathematical Center ‘Mathematics of Future Technologies’ (grant no. 075-02-2023-949).