Abstract
Here, for the first time, error estimation of the functions gin H_{z}^{(w)} and tilde{g}in H_{z}^{(w)} classes using 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.
Highlights
Several results on the error estimation of a function g in Lipschitz and Hölder classes by a trigonometric polynomial using different single and product means have been obtained by the researchers like [1,2,3,4,5,6,7,8,9,10,11], and [12].Our motivation for this work is to consider a more advanced class of functions that can provide best approximation by a trigonometric polynomial of degree not more than r
7 Conclusion Approximation by trigonometric polynomials is at the heart of approximation theory
Much of the advances in the theory of trigonometric approximation are due to the periodicity of the functions
Summary
Several results on the error estimation of a function g in Lipschitz and Hölder classes by a trigonometric polynomial using different single and product means have been obtained by the researchers like [1,2,3,4,5,6,7,8,9,10,11], and [12]. In this work, we generalize the results of Kushwaha and Dhakal [3] and Dhakal [1, 2]. We obtain the results on the error estimation for the function f ∈ Hz(w) (z ≥ 1) by T.C1 method by F. We obtain the results on the error estimation of the function g ∈ Hz(w) (z ≥ 1) by T.C1 method of C.
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