On the Degree of Approximation of Functions Belonging to the Lipschitz Class by (E, q)(C, α, β) Means

Abstract

In this paper two generalized theorems on the degree of approximation of conjugate functions belonging to the Lipschitz classes of the type $text{Lip}alpha $, $0<alpha leq 1$, and $W(L_{p},xi (t))$ are proved. The first one gives the degree of approximation with respect to the $L_{infty}$-norm, and the second one with respect to $L_{p}$-norm, $pgeq 1$. In addition, a correct condition in proving of the second mentioned theorem is employed.