QUANTITATIVE EQUI-UNIFORM APPROXIMATION PROCESSES OF INTEGRAL OPERATORS IN BANACH SPACES

Abstract

We give quantitative estimates of the rate of convergence of equiuniform approximation processes of integral operators in Banach spaces in terms of the modulus of continuity of functions to be approximated and higher order absolute moments of approximate kernels. Furthermore, applications are presented for various equi-uniform summation processes, interpolation type operators, convolution type operators, and several concrete examples of approximating operators are also provided.