On approximation of hexagonal Fourier series in the generalized Hölder metric

Abstract

Let f be an H-periodic continuous function. The approximation order of the function f by deferred Cesàro means of its hexagonal Fourier series is estimated in uniform and generalized Hölder metrics.

An analysis of the convergence problem of a function of hexagonal Fourier series in generalized Hölder norm using Hausdorff operator

“…The degree of approximation of function of hexagonal Fourier series in Lipschitz and generalized Hölder spaces using Cesàro and Abel was also studied by Guven [18, 19]. The degree of approximation of the function of hexagonal Fourier series in generalized Hölder spaces using matrix means was studied by Guven [20] and Aslan [21]. Very recently, Singh and Singh [1] obtained very important results on characterization of Hausdorff matrices and Nigam and Sah [22] obtained characterization results on double Hausdorff matrices.…”