In this paper we construct a linear and positive approximation process of discrete type which includes as a particular case the Meyer-Kong and Zeller operatros.
Based on several inequalities we prove that the sequence converges to the identity operator. We obtain inequalities regarding estimations of the remainder which are given by using the moduli of smoothness of first and second order as well as the Lipschitz type maximal function. also we establish that our operators have the variation diminishing property.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
O. Agratini, Korovkin type error estimates for Meyer-Konig and Zeller operators, Mathematical Inequalities and Applications, 4 (2001), 119-126
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Mathematical Inequalities and Applications
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 U. ABEL, The complete asymptotic expansion for the Meyer-Konig and Zeller Operators, Journal of Math. Analysis and Applications 208(1997), 109–119.
 J. A. H. ALKEMADE, The second moment for the Meyer-Konig and Zeller operators, J. Approx. Theory, 40(1984), 261–273.
 F. ALTOMARE AND M. CAMPITI, Korovkin-Type Approximation Theory and Its Applications, de Gruyter Series Studies in Mathematics, Vol.17, Walter de Gruyter, Berlin-New York, 1994.
 M. BECKER AND J. NESSEL, A global approximation theorem for Meyer-Konig and Zeller operators, Math. Z., 160(1978), 195–206.
 WENZHONG CHEN, On the integral type Meyer-Konig and Zeller operators, Approx. Theory and Its Applications, 2(1986), 3, 7–18.
 E. W. CHENEY AND A. SHARMA, Bernstein power series, Canad. J. Math., 16(1964), 241–253.
 OGUN DOGRU, Approximation order and asymptotic approximation for generalized Meyer-Konig and Zeller operators, Mathematica Balkanica, New Series vol. 12(1998), 3–4, 359–367.
 I. GAVREA AND I. RASA, Remarks on some quantitative Korovkin-type results, Revue d’Analyse Numer. et de Theorie de l’Approx., 22(1993), 2, 173–176.
 H. H. GONSKA, Quantitative Korovkin type theorems on simultaneous approximation, Math. Z., 186(1984), 419–433.
 XU JIHUA AND LI LUOQING, Converse theorems on approximation by integral type Meyer-Konig and Zeller Operators, in “Progress in Approximation Theory” (P. Nevai and A. Pinkus Eds.) Academic Press, Boston, 1991, 899–911.
 B. LENZE, On Lipschitz-type maximal functions and their smoothness spaces, Proc. Netherland Acad. Sci. A 91(1988), 53–63.
 A. LUPAS AND M. W. MULLER, Approximation properties of the Mn -operators, Aequationes Math., 5(1970), 19–37.
 M. W. MULLER, Lp -approximation by the method of integral Meyer-Konig and Zeller operators, Studia Math., 63(1978), 81–88.
 I. J. SCHOENBERG, On variation diminishing approximation methods, In: On Numerical Approximation (Proc. Sympos. Conducted by the MRC; ed. R. E. Langer), Madison, Univ. of Wisconsin Press 1959, 249–274.
 P. C. SIKKEMA, On some linear positive operators, Indag. Math., 32(1970), 327–337.
 V. TOTIK, Approximation by Meyer-Konig and Zeller type operators, Math. Z., 182(1983), 425–446