An improved estimate of the rate of convergence of the integrated Meyer- König and Zeller operators for functions of bounded variation (Q1340533)

Let \((\widehat M_ n)_{n \in \mathbb{N}}\) denote the method of Kantorovič type Meyer-König and Zeller operators for the approximation of functions \(f \in L_ 1 [0,1]\) in the \(L_ 1\)-metric. (The authors call the operators \(\widehat M_ n\) integrated Meyer- König and Zeller operators.) The main result of the paper is a pointwise estimate for the rate of convergence of this method for functions \(f \in BV [0,1]\) on intervals \(\delta \leq x \leq 1 - \delta\), \(\delta > 0\). The authors made some corrections in an earlier version of this theorem and its probabilistic proof by \textit{S. Guo} [J. Approximation Theory 56, No. 3, 245-255 (1989; Zbl 0677.41023)].