On some new operators of discrete type


In this paper we are dealing with a general class of linear and positive operators of discrete type. We investigate the convergence of the operators and we give estimates of the rate of convergence by using the classical modulus of continuit, Ditzian-Totik weighted moduli, as well as the weighted K-functional of second order. In some cases we prove that these operators leave invariant the class of increasing funcitons respectively the convex and the Holder continuous funcitons. also a Voronovskaja type formula is established and some concrete exemples are presented.


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


linear and positive operator; rate of convergence; Ditzian-Totik weighted modulus; Voronovskaya-type formula

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O. Agratini, On some operators of discrete type, Supllemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Proceedings of the 4th International Conference on Functional Analysis and Approximation Theory Acquafredda di Maratea, (Potenza-Italy), 68, 2000, pp. 229-243


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[1] F. Altomare, Approximation theory methods for the study of diffusion equations, in “Approximation Theory, Proc. IDoMAT 95” (Manfred W. Muller, M. Felten, Detlef H.Mach, Eds.), 9-26, Mathematical Research, vol. 86, Akademie Verlag, Berlin, 1995.
[2] F. Alomare, On some sequences of positive linear operators on unbounded intervalsI, in “Approximation and  Optimization, Proc. ICAOR 1996” (D.D. Stancu, Gh. Coman, W.W. Breckner, P. Blaga, Eds.), vol.1, 1-16, Transilvania Press, Cluj-Napoca, 1997.
[3] F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Applications, de Gruyter Series Studies in Mathematics, vol. 17, Walter de Gruyter & Co., Berlin, New York, 1994.
[4] F. Altomare and I. Carbone,  On a new sequence of positive linear operators on unbounded intervals,  Suppl. Rend. Circ. Mat. Palermo, 40 (1996), 2, 23-36.
[5] F. altomare and E.M. Mangino, On a genralization of Baskakov operators,  Rev. Roumaine Math. Pures Appl., 44(1999), 5-6, 683-705.
[6] I. Carbone, Shape preserving properties of some positive linear operatores on unbounded intervals, Journal of Approx. Theory, 93(1998), 140-156.
[7] Z. Ditzian and V. Totik,  Moduli of Smoothness,  Springer Series in Computtional  Mathematics, vol. 9, Springer-Verlag, New York Inc., 1987.
[8] M.K. Khan and M.A. Peters,  Lipschitz constants for some approximation operator of a Lipschitz continuous function, Journal of Approx. Theory, 59 (1989), 307-315.
[8] P.C.  Sikkema,  On some linear popsitive operators, Indagationes Mathematicae, 32(1970), 4, 327-337.


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