About characterization of one K-functional

We characterize the K-functional (K) over tilde (psi)(f, t)(p) (used in approximating functions by Durrmeyer and Kantorovich modifications of Baskakov operator) (K) over tilde (psi)(f, t)(p) = inf {parallel to f-g parallel to(p) +t parallel to(D) over tilde (g)parallel to(p) : f - g is an element of L-p [0, infinity), g is an element of(W) over tilde (p) [0, infinity)} where (D) over tilde = d/dx (x(1+x) d/dx), (W) over tilde (p) [0, infinity) = {f : f, f' is an element of AC(loc) (0,infinity), (D) over tildef is an element of L-p [0, infinity), lim(x -> 0+,) (infinity) psi(x) f'(x) = 0} by appropriate moduli of smoothness. (C) 2017 Elsevier Inc. All rights reserved.