Best approximation of functions in generalized Hölder class

Abstract

Abstract Here, for the first time, error estimation of the functions g∈Hz(w) $g\in H_{z}^{(w)}$ and g˜∈Hz(w) $\tilde{g}\in H_{z}^{(w)}$ classes using TC1 $TC^{1}$ method of F. S. (Fourier Series) and C. F. S. (Conjugate Fourier Series), respectively, are determined. The results of (Dhakal in Int. Math. Forum 5(35):1729–1735, 2010; Dhakal in Int. J. Eng. Technol. 2(3):1–15, 2013; Kushwaha and Dhakal in Nepal J. Sci. Technol. 14(2):117–122, 2013) become the particular cases of our Theorem 2.1. Some important corollaries are also deduced from our main theorems.

Keywords

• Best approximation
• Generalized Hölder class
• Matrix (T) means
• C 1 $C^{1}$ means
• T C 1 $TC^{1}$ means
• Fourier series