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| Widths theory is an essential part of the extremal theory of approximation. As a branch of widths, relative n-widths attracts the attention of researchers and has been studied a lot in resent years. In this paper, periodic function classes on regular hexagon and rectangle on the plane, and also their relationship have been considered first.Furthermore, using the iterate Laplace operator, a periodic differentiable class on regular hexagon is defined. Taking advantage of the relationship mentioned above, the asymptotic estimates of the relative n-width of the class of $L_2$ in $L_q$ metric is obtained. |
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| Keywords:approximation theory, relative n-widths, differentiable function classes, regular hexagon |
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