Approximation by families of generalized sampling series, realizations of generalized kappa-functionals and generalized moduli of smoothness

摘要

We study properties of realizations of generalized K-functionals and generalized moduli of smoothness in L-p(R-d) spaces with 0 < p < infinity as well as in the space C(R-d) of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between the approximation error of families of generalized sampling series generated by an arbitrary generator with compact support, realizations of generalized kappa-functionals generated by homogeneous functions and generalized moduli of smoothness generated by a periodic function. Our approach covers classical approximation methods, kappa-functionals related to fractional derivatives and fractional moduli of smoothness. (C) 2020 Elsevier Inc. All rights reserved.