Promotion Of Meyer,-k-(?) Nig-zeller, Type Operator Approximation Theorem

The study of direct and inverse theorems on the approximation of linearoperators to functions in normed linear spaces is an important subject in theapproximation theory．It is significant in theory and application．In this paperwe use Ditzian-Totik modulus of smoothnessω_?(f,t)_p(1≤p≤∞)to studyapproximation direct theorem and equivalent theorem for Meyer-k(o|¨)nig-Zelleroperator,obtain the equivalence theorem for generalized Meyer-k(o|¨)nig and Zellertype operators in the space L_p(1≤p≤∝)with Ditzian-Totik modulus．Theresult is following:Theorem For f∈L_p[0,1)(1≤p≤∞),0<β<1,(?)(x)=x^1/2(1-x),the following statement are equivalentwhereω_?(f,t)_p is Ditzian-Totik modulous．...