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

摘要

The aim of this paper is to study the behavior of the operators T{sub}λ defined by T{sub}λ(f;x) = ∫(K{sub}μ(t-x,f(t))dt) (from a to b), x∈. Here we estimate the rate of convergence at a point x, which has a discontinuity of the first kind as λ → λ{sub}0. 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.