Approximation of the function $\bf{f \in Lip (\alpha, p)}$ using infinite matrices of Ces´aro submethod

  • Smita Sonker
  • Alka Munjal


The analysis of error estimation $E_n(f)$ of trigonometric Fourier approximation are of a great interest since last few decades due to an important use in designing the digital filters. In this paper, we have approximated the signals by trigonometric polynomial in $Lip(\alpha, p)$ and found the approximation degree by using a more general $C_\lambda$- method and reducing the conditions of monotonicity. Our theorems give the error estimation in term of  $\lambda(n)$ $\big\lbrace\big(\lambda(n)\big)^{-\alpha}< n^{-\alpha}, 0<\alpha\leq1 \big\rbrace$, which sharpen the previous results. By reducing the restrictions of the filter,  we can improve the functions of the filter (like Automatic compensation, permanently unit power factor, overcome of unbalancing situation, etc.).