Functions from $L_p$-spaces and Taylor means

Abstract

In this paper, we take up Taylor means to study the degree of approximation of $fın L_p$ ($p\ge1$) under the $L_p$-normand obtain a general theorem which is used to obtain four more theorems that improve some earlier results obtained by Mohapatra, Holland andSahney [J. Approx. Theory 45 (1985), 363–374]. One of our theorems provides the Jackson order as the degree of approximation for a subspace of$Lip(\a,p)$ ($0<\a<1$, $p\ge1$) and generalizes a result due to Chui and Holland [J. Approx. Theory 39 (1983), 24–38].