On approximation of hexagonal fourier series

Abstract

Let the function f belong to the Holder class H-alpha(Omega) over bar , 0 < alpha <= 1, where Omega is the spectral set of the hexagonal lattice in the Euclidean plane : Also, let p = (p(n)) and q = (q(n)) be two sequences of non-negative real numbers such that p(n) < q(n) and q(n) -> infinity as n -> infinity. The order of approximation of f by deferred Cesaro means D-n (p, q; f) of its hexagonal Fourier series is estimated in the uniform and Holder norms.