On Approximation by Matrix Means of the Multiple Fourier Series in the Hölder Metric

Abstract

In this work, we shall give the degree of approximation for functions belonging to Hölder class by matrix summability method of multiple Fourier series in the Hölder metric.

On approximation of functions, conjugate to the functions of several variables belonging to weighted Lipschitz and Zygmund classes

“…2) is said to be summable to s 1 by the N -multiple matrix means. The regularity conditions of the N -multiple matrix means are same as given in [2]. We can obtain particular cases of N -multiple matrix means by changing (a km,im ), for each m ∈ M , as given in section 2.…”

Approximation by double second type delayed arithmetic mean of periodic functions in $H_{p}^{(ω, ω)}$ space

“…For one dimension, a degree of approximation of a function in the space H (ω) p has been given by several authors, see [1,2,3,4,6,8,11,13,16] and some other references already mentioned here. Inspired by these papers, we have given two corresponding results using the second (even) type double delayed arithmetic means of the Fourier series of a function from the space H (ω,ω) p (H (ω,ω) p;β1,β2 ).…”

“…On the other hand, results on approximation of bivariate integrable functions and 2πperiodic in each variable by their double Fourier series in the Hölder metric, the interested reader can find in [4], [9] and [14]. In all results reported in these papers, we came across to the degree of approximation of functions by various means of their double Fourier series and in which the quantity of the form O(log n) appears.…”