Posts by Octavian Agratini

Abstract

The concern of this note is to introduce a general class of linear positive operators of discrete type acting on the space of real valued functions defined on a plane domain. These operators preserve some test functions of Bohman-Korovkin theorem. Following our technique, as a particular class, a modified variant of the bivariate Bernstein-Chlodovsky operators is presented.

Authors

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

Keywords

linear positive operator, Bohman-Korovkin theorem, bivariate modulus of smoothness, Bernstein-Chlodovsky operator.

Paper coordinates

O. Agratini, On a class of linear positive bivariate operators of King type, Studia Universitatis Babes-Bolyai, Mathematica, 51 (2006) no. 4, pp. 13-22.

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About this paper

Journal

Studia Universitatis Babes-Bolyai, Mathematica

Publisher Name
DOI
Print ISSN

1843-3855

Online ISSN

2065-9490

google scholar link

[1] Agratini, O., Linear operators that preserve some test functions, International Journal of Mathematics and Mathematical Sciences, Volume 2006, Article ID94136, Pages 1-11, DOI 10.1155/IJJMS.

[2] Altomare, F. and Campiti, M., Korovkin-type Approximation Theory and its Applications, de Gruyter Studies in Mathematics, Vol.17, Walter de Gruyter, Berlin, 1994.

[3] Chlodovsky, I., Sur le developpment des fonctions definies dans un intervalle infini en series de polynomes de M.S. Bernstein, Compositio Math. 4(1937), 380-393.

[4] Duman, O. and Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(2006), f.1-2, 33-46.

[5] Gonska, H. and Pit¸ul, P., Remarks on an article of J.P. King, Schriftenreihe des Fachbereichs Mathematik, Nr.596(2005), Universit¨at Duisburg-Essen, 1-8.

[6] Gurdek, M., Rempulska, L. and Skorupka, M., The Baskakov operators for functions of two variables, Collect. Math., 50(1999), f.3, 289-302.

[7] Ipatov, A.F., Estimate of the error and order of approximation of functions of two variables by S.N. Berstein’s polynomials (in Russian), Uˇc. Zap. Petrozavodsk Univ., 4(1955), f.4, 31-48.

[8] King, J.P., Positive linear operators which preserve x2, Acta Math. Hungar., 99(2003), no.3, 203-208.

[9] Totik, V., Uniform approximation by Sz´asz-Mirakjan type operators, Acta Math. Hung., 41(1983), f.3-4, 291-307.

[10] Volkov, V.I., On the convergence of sequences of linear positive operators in the space of continuous functions of two variables (in Russian), Dokl. Akad. Nauk SSSR (N.S.), 115(1957), 17-19.

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