On the uniform modulus of continuity of the operator of best approximation in the space of periodic functions

Introducion and preliminary results In this paper we shall present some results connected with the uniform continuity of best approximations. In the last fifteen years problems dealing with local continuity of best approximation have been widely investigated. It was proved ([1], [2]) that the metric projection operator onto a finite-dimensional ~ebysev subspace of C[a, b] is pointwise Lip 1. An analogous result was obtained for the space Lp, 2 0 and Me= C[a, b] we can introduce the uniform modulus of continuity of the operator of best approximation on M as