On the Convergence for a Class of Odd TrigonometricInterpolation Polynomial Operators

The paper introduces an odd Trigonometric polynomial operator H _n(f:r,x)(where r is a given natural number)based on these values of f(x)(where f(x)∈C _2πand f(x)are even functions)on these nodes(x _k=(kπ)/(n+1)) ⁿ _k=1. H _n(f:r,x)uniformly converge to f(x)on the total real axis. The approximation order of H _n(f:r,x)reaches the rest approximation order when used to approximate to f(x)wheref(x)∈C _2π,(0 SymbolcB@ j SymbolcB@ r-1)and f(x)is odd function