On some extremal problems in the theory of approximation of functions in the spaces S^p,1 ≤ p < ∞ - Vakarchuk, S. B.; Shchitov, A. N. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We consider and study properties of the smoothness characteristics Ω_m(f, t)_S^p,m N,t > 0, of functions f(x) that belong to the space S^p,1 ≤ p < ∞, introduced by Stepanets. Exact inequalities of the Jackson type are obtained, and the exact values of the widths of the classes of functions defined by using Ω_m(f, t)_S^p,m N,t > 0 are calculated.