On the Convergence for a Class of Odd Trigonometric Interpolation Polynomial Operators

The paper introduces an odd Trigonometric polynomial operator Hn(f:r,x)(where ris a given natural number)based on these values of f(x)(where f(x) ∈C2π and f(x) are even functions) on these nodes (xk=kπ/n+1)n k=1.Hn(f:r,x) uniformly converge to f(x)on the total real axis.The approximation order of Hn(f:r,x)reaches the rest approximation order when used to approximate to f(x) where f(x) ∈C2π,(0≤j≤r-1)and f(x) is odd function