Korovkin type error estimates for Meyer-König and Zeller operators (Q2711484)

On the space \(C[0,a]\), \(0<a<1\), a new sequence of positive linear operators is introduced generalizing in a certain sense the Meyer-König and Zeller operators. By Korovkin's theorem it is proved that this sequence is an approximation method on \(C[0,a]\) in the uniform norm on \([0,a]\). The local approximation error is estimated on the one hand in terms of an expression containing the classical modulus of continuity as well as the classical second order modulus of smoothness and on the other hand in terms of the Lipschitz-type maximal function of order \(\alpha\in(0,1]\) which was introduced by B. Lenze. Finally the variation diminishing property is established.