On pointwise convergence estimates for positive linear operators on C[a, b]

AbstractThis note is concerned with positive linear approximation processes φn(f; t) (n = 1, 2, …) on C[a, b] which are exact for the functions l, t. A short proof will be given for the pointwise estimate of |f(t) − φn(f; t)| (t ∈ [a, b]) in terms of the second modulus of continuity, i.e. with increment depending on t