Approximation of functions in generalized Zygmund class by double Hausdorff matrix

Abstract

Abstract In the present work, we emphasize, for the first time, the error estimation of a two-variable function g ( y , z ) $g(y,z)$ in the generalized Zygmund class Y r ( ξ ) $Y_{r}^{(\xi )}$ ( r ≥ 1 $r\geq 1$ ) using the double Hausdorff matrix means of its double Fourier series. In fact, in this work, we establish two theorems on error estimation of a two-variable function of g in the generalized Zygmund class.

Keywords

• Error estimation
• Generalized Zygmund class
• Double Hausdorff ( Δ H p q ) $(\Delta _{H_{pq}})$ summability means
• Double Fourier series (DFS)