Kantorovich-type operators preserving affine functions


Starting from positive linear operators which have the capability to reproduce affine functions, we design integral operators of Kantorovichtype which enjoy by the same property. We focus to show that the error of approximation can be smaller than in classical Kantorovich construction on some subintervals of its domain. Special cases are presented


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


Szász-Mirakjan operator, Baskakov operator, Stancu operator, Kantorovich operator, modulus of continuity.

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O. Agratini, Kantorovich-type operators preserving affine functions, Hacettepe Journal of Mathematics and Statistics, 45 (2016) no. 6, pp. 1657-1663. 


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Hacettepe Journal of Mathematics and Statistics

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[1] Butzer, P.L., On the extensions of Bernstein polynomials to the innite interval, Proc. Amer. Math. Soc., 5(1954), 547-553.
[2] Ditzian, Z., Totik, V., Moduli of Smoothness, Springer-Verlag, New York Inc., 1987.
[3] Duman, O., Özarslan, M.A., Della Vecchia, B., Modied Szász-Mirakjan-Kantorovich operators preserving linear functions, Turk. J. Math., 33(2009), 151-158.
[4] Kantorovich, L.V., Sur certains développement suivant les polynômes de la forme de S. Bernstein, I, II, C.R. Acad. URSS (1930), 563-568, 595-600.
[5] Razi, Q., Approximation of a function by Kantorovich-type operators, Matematicki Vesnik, 41(1989), 183-192.
[6] Shisa, O., Mond, B., The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. USA, 60(1968), 1196-1200.
[7] Stancu, D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumanie Math. Pures Appl., 8(1968), 1173-1194

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