Meyer,-k (?) Nig-zeller,-b¨¦zier Operator Approximation Theorem

The theory of operator's approximation mainly studies the convergent prop-erties and convergence rate of a sequence of linear operators and other relativeproblems．The study of direct and inverse theorems and equivalent theorems ofsome well-known linear operators(such as Bernstein,Baskakov operators)andtheir modification of Durrmeyer and Kantorovich is an important research pro-gram in the theory of operator's approximation．Recently B(?)zier-type operatorswere introduced and studied elementarily,but it is necessary to study these op-erators deeply with its using field wider and wider．In this paper,we will mainlydiscuss the approximate properties of Meyer-k(o|¨)nig-Zeller-B(?)zier operators byusing the unified modulusω_(?)^λ(f,t)_∞,and obtain some results which are asfollows:Theorem A If f∈C[0,1)is bounded,(?)(x)=x^1/2(1-x),0≤λ≤1,wehave |M_n,α(f,x)-f(x)|≤Cω_?^λ(f,(?)^1-λ(x)/n^1/2)．Theorem B For 0≤λ≤1,(?)(x)=x^1/2(1-x),f∈C[0,1),‖f‖<∞,0<β<1,we have |M_n,α(f,x)-f(x)|=O(((?)^1-λ(x)/n^1/2)^β)impliesω_?^λ(f,t)=O(t^β)．...