On Approximation of Hexagonal Fourier Series

Ali Guven

Abstract


Let the function $f$\ belong to the H\"{o}lder class $%H^{\alpha }\left( \overline{{\small \Omega }}\right) ,$ $0<\alpha \leq 1,$\where $\Omega $\ is the spectral set of the hexagonal lattice in the Euclideanplane$.$ Also, let $p=\left( p_{n}\right) $ and $q=\left( q_{n}\right) $ betwo sequences of non-negative real numbers such that $p_{n}<q_{n}$ and $%q_{n}\rightarrow \infty $ as $n\rightarrow \infty .$\ The order ofapproximation of $f$\ by deferred Ces\`{a}ro means $D_{n}\left( p,q;f\right) $ of its hexagonal Fourier series is estimated in the uniform and H\"{o}ldernorms.

Keywords


Deferred Ces\`{a}ro means, Hexagonal Fourier series, Holder class

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