Characterization of Best Algebraic Approximation by an Algebraic Modulus of Smoothness Original Research Article

The author introduced in an earlier paper a modulus of smoothness for nonperiodic functions based on an algebraic addition ⊕ defined on [−1, 1]. In this paper the Steklov functions and an equivalentK-functional are given. Moreover, a characterization of best approximation by algebraic polynomials and the equivalence between the algebraic modulus and the Butzer–Stens modulus, introduced by the Chebyshev translation method, are shown.