An Improved Estimate of the Rate of Convergence of the Integrated Meyer-König and Zeller Operators for Functions of Bounded Variation

Bojanic [Publ. Inst. Math. (Beograd) (N.S.) 26 (40) (1979), 57-60] gave an estimate of the rate of convergence for Fourier series of functions of bounded variation. Cheng [J. Approx. Theory39 (1983), 259-274] gave the result of this type for the Bernstein operator. Recently, Guo [J. Approx. Theory56 (1989), 245-255] used the results of probability theory to arrive at an estimate for the rate of convergence of the nth integrated Meyer-König and Zeller operator M̂n, n∈N (Maier et al. [J. Approx. Theory32 (1981), 27-31]) for a real-valued Lebesgue integrable function ƒ of bounded variation defined on I = [0, 1]. We have been able to correct and improve Guo′s estimate, while using parts of his work. This paper was in the first place motivated by some misprints in S. Guo′s paper.