Rate of convergence of nonlinear integral operators for functions of bounded variation

The aim of this paper is to study the behavior of the operators Tλ defined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T_\lambda (f;x) = \int\limits_a^b {K_\lambda (t - x,f(t))dt,x \in < a,b > .} $$\end{document}. Here we estimate the rate of convergence at a point x, which has a discontinuity of the first kind as λ → λ0. This study is an extension of the papers [9] and [13], which includes Bernstein operators. Beta operators, Picard operators, Philips operators, Durrmeyer operators, etc. as special cases.