Degree of Approximation of Function $f\in H_p^{(w)}$ Class in Generalized Hölder Metric by Matrix Means

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

“…Moreover, Deǧer [3] determined the degree of approximation of functions by matrix means of their Fourier series in the same space of functions introduced in [2]. In particular, he extended some results of Leindler [11] and some other results by weakening the monotonicity conditions in the results obtained by Singh and Sonker [16] for some classes of numerical sequences introduced by Mohapatra and Szal [12]. Leindler's results obtained in [11], are generalized in [8] by first author of the present paper, for functions from a Banach space, mainly using the generalized Nörlund and Riesz means.…”

“…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 ).…”