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In the present paper, we establish a theorem on best approximation of a function g 2 Bλ q (Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1. [ABSTRACT FROM AUTHOR]

In this paper, we have proved some results on the degree of approximation in sup-norm of continuous functions by generalized deferred Voronoi-Norlund means of partial sums of their Fourier series. [ABSTRACT FROM AUTHOR]

The problem of obtaining degree of approximation for the 2π-periodic functions in the weighted Lipschitz class W(Lp; ξ(t)) (p ≥ 1) by Riesz means of the Fourier series have been studied by various investigators under Lp-norm. Recently, Deepmala and Piscoran [Approximation of signals(functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series, J. Inequal. Appl., (2016), 2016:163. DOI 10.1186/s13660-016-1101-5] obtained a result on degree of approximation for weighted Lipschitz class by Riesz means. In this note, we extend this study to the weighted Lp-norm which in turn improves some of the previous results. We also derive some corollaries from our result. [ABSTRACT FROM AUTHOR]

Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the W(Lr, ξ(t))-class by (..., pn, qn)(E, s)-product summability means of a Fourier series. The result obtained here, generalizes several known theorems. [ABSTRACT FROM AUTHOR]

In this paper, we have proved the degree of approximation of functions belonging to L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series at x = 0. The aim of this paper is to concentrate on the approximation properties of the functions in L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series associated with the function f. [ABSTRACT FROM AUTHOR]

The results corresponding to some theorems of S. Lal [Appl. Math. Comput. 209 (2009), 346-350] and the results of the authors [In: Banach Center Publ. 95, Polish Acad. Sci. Inst. Math., Warsaw, 2011, pp. 339-351] are shown. The same degrees of pointwise approximation as in mentioned papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results the estimation on norm approximation are derived. Some special cases as corollaries are also formulated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the degree of approximation of a function f that is a conjugate of a function f belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series. [ABSTRACT FROM AUTHOR]

This note exhibits, as an example, that integral-type conditions can be replaced by sequence-type assumptions in four theorems pertaining to P. Chandra's theorem and its generalizations. [ABSTRACT FROM AUTHOR]

We prove the results generalized and improved of some theorems of X. Z. Krasniqi [] on pointwise approximation of integrable functions and their conjugate by matrix means of Fourier series and its conjugate. [ABSTRACT FROM AUTHOR]

In this paper, a new estimate for the degree of approximation of a function f(x; y) belonging to generalized Lipschitz class Lip(ξ1, ξ2) by (N, pm, qn) summability method of its double Fourier series has been determined. [ABSTRACT FROM AUTHOR]

Abstract: Analysis of signals or time functions are of great importance, because it convey information or attributes of some phenomenon. In this paper, we consider the functions/signals defined in terms of their integral modulus of continuity and approximate them by matrix means of their trigonometric Fourier series. The error of approximation obtained in this paper depends on the integral modulus of continuity of the signal. We also discuss an example to show the application of the result in the situation when the Fourier series of the signal has Gibbs phenomenon. We also discuss some corollaries of our theorems. [Copyright &y& Elsevier]

Abstract: In the present paper, a new theorem on the degree of approximation of function conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz -class by dropping the monotonicity condition on the generating sequence {pn } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22]. [Copyright &y& Elsevier]

In the present study, a new theorem on the degree of approximation of function f, conjugate to a periodic function f belonging to weighted W(Lr, ξ(t))-class using semimonotonicity on the generating sequence {pn} has been established. [ABSTRACT FROM AUTHOR]

In the present paper, a new theorem on the degree of approximation of a function [InlineEquation not available: see fulltext.], conjugate to a 2 π periodic function f belonging to the Lip α ([InlineEquation not available: see fulltext.]) class without the monotonicity condition on the generating sequence [InlineEquation not available: see fulltext.] has been established, which in turn generalizes the results of Lal (Appl. Math. Comput. 209: 346-350, 2009) on a Fourier series. MSC: 40G05, 41A10, 42B05, 42B08. [ABSTRACT FROM AUTHOR]

Very recently, Sonker and Singh [21] determined the degree of approximation of the conjugate of 2π-periodic signals (functions) belonging to Lip(α, r)(0 < α = 1, r = 1)-class by using Cesàro-Euler (C,1) (E,q) means of their conjugate trigonometric Fourier series. In the present paper, we generalize the result of Sonker and Singh [21] on the generalized weighted Lipschitz W(Lr, ξ(t)), (r = 1)- class of signals (functions) by product summability (C,1) (E,q) transform of conjugate trigonometric Fourier series. Our result also generalizes the result of Lal and Singh [6]. Few applications and example of approximation of functions will also be highlighted. [ABSTRACT FROM AUTHOR]

Recently, Lal [9] has determined the degree of approximation of function belonging to Lip α and weighted classes using Product C¹. Np summability with non-increasing weights{pn}. In this paper, we determine the degree of approximation of function f, conjugate to a 2π-periodic function f belonging to Lip (ξ (t), r)-class using semi-monotonicity on the generating sequence {pn} with proper set of conditions. Few applications of approximation of functions will also be highlighted. [ABSTRACT FROM AUTHOR]

In this paper a theorem on degree of approximation of a function f ∈ Lip(ξ(t),r) by product summability (E,q)(N,pn) of Fourier series associated with f has been established. [ABSTRACT FROM AUTHOR]

In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α, r), 1 ≤ r < ∞ and the weighted class W(Lr, ξ(t)), 1 ≤ r < ⊂ by (C, 2)(E, 1) product operators have been obtained. The results obtained in the present paper generalize various known results on single operators. [ABSTRACT FROM AUTHOR]

We generalize some results on the degree of approximation of continuous functions by means of Fourier series, which were obtained by Chandra ([1, 2]) and Leindler ((4]). Some applications of the main results are given. [ABSTRACT FROM AUTHOR]

In this paper, two quite new theorems on degree of approximation of conjugate of functions f ϵ Lipα class and f ϵ W (Lr, ξ(t)) class using (E,1) (C,1) product summability means of conjugate Fourier series have been established. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper Lal and Yadov obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions. [Copyright &y& Elsevier]

Abstract: The paper presents a method for establishing direct and strong converse inequalities in terms of -functionals for convolution operators acting in homogeneous Banach spaces of multivariate functions. The method is based on the behaviour of the Fourier transform of the kernel of the convolution operator. [Copyright &y& Elsevier]

Abstract: In this paper, two new theorems on the degree of approximation of the function f ∈Lipα and f ∈ W(L r , ξ(t)) have been established. [Copyright &y& Elsevier]

Recently, L.N. Mishra et al. obtained a new theorem on the degree of approximation of function f ̃ : conjugate to a 2 π periodic function f belonging to the generalized weighted Lipschitz W ( L r , ξ ( t ) ) ( r ⩾ 1 ) -class (Mishra et al., 2014). In this note, we point out that the conclusion of the theorem only holds for the constant functions, and thus the result is trivial. [ABSTRACT FROM AUTHOR]