Approximation of functions by nonlinear singular integral operators depending on two parameters

Eugeniusz Wachnicki; Grażyna Krech

2018/92/3-4 (15) — DOI: 10.5486/PMD.2018.8080 — pp. 481-494

Approximation of functions by nonlinear singular integral operators depending on two parameters

Authors: Eugeniusz Wachnicki and Grażyna Krech

Abstract:

The aim of this paper is to study the behavior of nonlinear singular integral operators of the form $$ T_w(f)(s)=\int_{G}K_w(s-t,f(t))dt. $$ Here, we estimate the rate of convergence at a point $s_0$ in which a function $f$ is continuous. This is an extension of the paper by Świderski and Wachnicki [21].

Keywords: rate of convergence, Voronovskaya-type theorem, nonlinear singular operators, locally compact groups, Haar integral

Mathematics Subject Classification: 41A25, 41A36, 47Hxx, 47G10, 28C10, 41A35