Operators generated by a quasi-scaling type function


In this paper we introduce linear approximation operators by using a scaling type function and a general bi-dimensional net. By using the first modulus of smoothness we establish Jackson type inequalities. For a new class of general integral type operators sufficient conditions are given both for shift invariance and for preservation of the global smoothness. Under additonal assumptions, our sequence becomes an approximation process. Also, some examples are provided and the particular case of Holder continuous functions is considered.


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


linear positive operator; modulus of smoothness, Jackosn-type inequalities; approximation process.

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O. Agratini, Operators generated by a quasi-scaling type function, Revista de la Union Matematica Argentina, 44 (2003) no. 2, pp. 21-30.


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Revista de la Union Matematica Argentina

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Union Matematica Argentina

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[1] Agratini, O., On some wavelet type linear operators, Proceedings of the International Symposium on Numerical Analysis and Approximation Theory, Cluj-Napoca, 9–11 May, 2002 (Ed. R. Trîmbiţaş), pp. 46–53, Presa Universitară Clujeană, 2002. MR2006922
[2] Altomare, F., Campiti, M., Korovkin-type Approximation Theory and its Applications, de Gruyter Series Studies in Mathematics, Vol. 17, Walter de Gruyter & Co., Berlin, New York, 1994. MR1292247
[3] Anastassiou, G., Quantitative Approximations, Chapman & Hall/CRC, Boca Raton, 2001. MR1791688
[4] Anastassiou, G., Gonska, H. H., On some shift invariant integral operators, univariate case, Annales Polonici Mathematici61(1995), 3, 225–243. MR1333249
[5] Anastassiou, G., Yu, X. M., Monotone and probabilistic wavelet approximation, Stochastic Anal. Appl.10(1992), 251–264. MR1166787
[6] Meyer, Y., Wavelets – Algorithms and Applications, SIAM, Philadelphia, PA, 1993. MR1219953


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