More than a summing up about Meyer-Konig and Zeller operators


In this paper we bring together the most outstanding results concerning the Meyer-Konig and Zeller operators. Furthermore, a generalization of these operators is presented establishing the degree of approximation in terms of the moduli of smoothness of first and second order. Also, the Ditzian-Totik modulus and the weighted K-functional are used.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Meyer-Konig and Zeller operator; modulus of smoothness; Ditzian-Totik modulus, K-functional

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O. Agratini, More than a summing up about Meyer-Konig and Zeller operators, Proceedings of the 4th Romanian-German Seminar on Approximation Theory and its Applications, Brasov, 3-5 July, 2000, pp.13-25, Duisburg: Schriftenreihe des Fachbereichs der Gerhard-Mercator-Universitat, SM-DU-48


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Schriftenreihe des Fachbereichs des Gerhard-Marcator-Universitat

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[1] U. Abel, The moments for the Meyer-Konig and Zeller operatros,  J. Approx. Theory 82 (1995), 352-361.
[2] U. Abel, The complete asymptotic expansion for the Meyer-Konig and Zeller operators,  J. Math. Anal. Appl. 208 (1997), 109-119.
[3] O. Agratini,  Korovkin type error estimates for  Meyer-Konig and Zeller operators,  Math. Ineq. Appl. 3 (2000) (in print).
[4] J.A.H. Alkemade,  The second moment for the Meyer-Konig and Zeller operators,  J. Approx. Theory 40 (1984), 261-273.
[5] F. Altomare, M. Campiti,  Korovkin-Type Approximation Theory and its Applications. Berlin et al: Walter de Gruyter 1994.
[6] M. Becker, R.J. Nessel,  A global approximation theorem for Meyer-Konig and Zeller operators,  Math. Z. 160 (1978), 195-206.
[7] E.W. Cheney, A. Sharma, Bernstein power series,  Canad. J. Math. 16 (1964), 241-253.
[8] Z. Ditzian, V. Totik, Moduli of Smoothness,  New York et al.: Springer Verlat 1987.
[9] Ogun Dogru, Approximation order and asymptotic approximation for generalized Meyer-Konig and Zeller operators, Math. Balk., New Ser. 12 (1998), 3-4, 359-367.
[10] M. Felten, Local and global approximation theorems for positive operators, J. Approx. Theory 94 (1998), 396-419.
[11] H.H. Gonska,  Quantitative Korovkin type theorems on simultaneous approximation,  Math. Z. 186 (1984), 419-433.
[12] A. Lupas and M.W.Muller, Approximation properties of the M_{n}-operators, Aequationes Math. 5 (1970), 19-37.
[13] W. Meyer-Konig and K. Zeller,  Bernsteinsch Potenzreihen, Studia Math. 19 (1960), 89-94.
[14] M.W.Muller, Die Folge der Gammaoperatoren,  Dissertation, Universitat Stuttgart 1967.
[15] T. Popoviciu,  Les fonctions convexes, Paris, Hermann & Cie 1944.
[16] P.C. Sikkema, On the asymptotic approximation with operators of Meyer-Konig and Zeller, Indag. Math. 32 (1970), 428-440.
[17] V. Totik, Uniform approximation by Baskakov and Meyer-Konig and Zeller operators,  Period. Math.Hung. 14 (1983), 209-228.


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