On degree of approximation of function by Voronoi means of its Fourier integral

The theorem on the degree of approximation to continuous function $f(x) \in L(-\infty; \infty)$ by Voronoi means of its Fourier integral is proved.

Monotonicity of sequence of the best approximating constants for the function $\sqrt{t}$

It is proved that the sequence of the constants of the best approximation of function $\sqrt{t}$ is monotone decreasing.

Approximation of function using generalized Zygmund class

In this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approximation of a function g in the generalized Zygmund space and resolve the issue of these works. We also determine the best error approximation of the functions g and $g^{\prime }$ g ′ , where $g^{\prime }$ g ′ is a derived function of a 2π-periodic function g, in the generalized Zygmund class $X_{z}^{(\eta )}$ X z ( η ) , $z\geq 1$ z ≥ 1 , using matrix-Cesàro $(TC^{\delta })$ ( T C δ ) means of its Fourier series and its derived Fourier series, respectively. Theorem 2.1 of the present paper generalizes eight earlier results, which become its particular cases. Thus, the results of (Dhakal in Int. Math. Forum 5(35):1729–1735, 2010; Dhakal in Int. J. Eng. Technol. 2(3):1–15, 2013; Nigam in Surv. Math. Appl. 5:113–122, 2010; Nigam in Commun. Appl. Anal. 14(4):607–614, 2010; Nigam and Sharma in Kyungpook Math. J. 50:545–556, 2010; Nigam and Sharma in Int. J. Pure Appl. Math. 70(6):775–784, 2011; Kushwaha and Dhakal in Nepal J. Sci. Technol. 14(2):117–122, 2013; Shrivastava et al. in IOSR J. Math. 10(1 Ver. I):39–41, 2014) become particular cases of our Theorem 2.1. Several corollaries are also deduced from our Theorem 2.1.

On degree of approximation of Fourier series of functions in Besov space using Norlund meanIn the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of Trigonometric Fourier series

In the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of Trigonometric Fourier series

On Approximation of Signals in the Generalized Zygmund Class Using (E,r)(N,qn) Mean of Conjugate Derived Fourier Series

In the present article, we have established a result on degree of approximation of function in the generalized Zygmund class Zl(m),(l ≥ 1) by (E,r)(N,qn)- mean of conjugate derived Fourier series.

Approximation of function belonging to generalized Hölder’s class by first and second kind Chebyshev wavelets and their applications in the solutions of Abel’s integral equations

In this paper, first and second kind Chebyshev wavelets are studied. New estimators $$E_{2^{k-1},0}^{(1)}$$ E 2 k - 1 , 0 ( 1 ) , $$E_{2^{k-1},M}^{(2)}$$ E 2 k - 1 , M ( 2 ) , $$E_{2^{k-1},0}^{(3)}$$ E 2 k - 1 , 0 ( 3 ) , $$E_{2^{k-1},M}^{(4)}$$ E 2 k - 1 , M ( 4 ) for first kind Chebyshev wavelets and estimators $$E_{2^{k},0}^{(5)}$$ E 2 k , 0 ( 5 ) , $$E_{2^{k},M}^{(6)}$$ E 2 k , M ( 6 ) , $$E_{2^{k},0}^{(7)}$$ E 2 k , 0 ( 7 ) and $$E_{2^{k},M}^{(8)}$$ E 2 k , M ( 8 ) for second kind Chebyshev wavelets for a function f belonging to generalized H$$\ddot{o}$$ o ¨ lder’s class have been obtained. Also, a method based on first and second kind Chebyshev wavelet approximations has been presented for solving integral equations. Comparison of solutions obtained by both wavelets method has been studied. It is found that second kind Chebyshev wavelet method gives better and accurate solutions as compared to first kind Chebyshev wavelet method. This is a significant achievement of this research paper in wavelet analysis.

On the Degree of Approximation of a Function by Nörlund Means of its Fourier Laguerre Series

In this paper, we have proved the degree of approximation of function belonging to L[0, ∞) by Nörlund Summability of Fourier-Laguerre series at the end point x = 0. The purpose of this paper is to concentrate on the approximation relations of the function in L[0, ∞) by Nörlund Summability of Fourier- Laguerre series associate with the given function motivated by the works [3], [9] and [13].

Approximation of Function in generalized Hölder Class

IIn the present work, we study error estimation of a function g ∈ H(η) r (r ≥ 1) class using Matrix-Hausdorff (T ∆H) means of its Fourier series. Our Theorem 1 generalizes twelve previously known results. Thus, the results of [4-5, 11–16, 18, 26, 29-30] become the particular cases of our Theorem 1. Several useful results in the form of corollaries are also deduced from our Theorem 1.