Abstract
Based on the probabilistic theory, the paper contains local estimates of the rate of convergence for contraction~\(C_{0}\)-semigroup. Simultaneously a class of linear positive operators of Feller-Stancu type is introduced, and the local and global rate of convergence for continuous functions is studied.
Authors
Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Contraction C₀-semigroup; approximation processes; moduli of smoothness, K-functional.
Paper coordinates
O. Agratini, On the rate of convergence for semigroups and processes of Feller type, Analele Universitatii Bucuresti, Matematica-Informatica, 51 (2002) no. 1, 3-11.
About this paper
Journal
Analele Universității București
Publisher Name
DOI
Print ISSN
2067-9009
Online ISSN
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[1] Agratini, O., Approximation by linear operators, Presa Universitară Clujeană, 2000.
[2] Altomare, F., Campiti, M., Korokvin-type Approximation Theory and its Applications, de Gryter Series Studies in Mathematics, vol. 17, Walter de Gruyter Co., Berlin, New York, 1994.
[3] Butzer, P.L., Berens, H., Semi-Groups of Operators and Approximation,SpringerVerlag,Berlin,1967.
[4] Butzer, P.L., Hahn, L., A probabilistic approach to representation formulae for semigroups of operators with rates of convergence, Semigroup Forum, vol. 21, 1980, pp. 257-272.
[5] Khan, M.K., On the Rate of Convergence of Bernstein Power Series fo rFunctions of Bounded Variation, J.Approx.Theory,57,1989,90-103.
[6] Rașa,I.,Vladislav,T., Analiză Numerică. Aproximare, problema lui Cauchy abstractă, proiectori Altomare, Editura Tehnică, București, 1999.
[7] Stancu, D.D., Use of probabilistic method in the theory of uniform approximation of continuous functions, Rev. Roum. Pures. et Appl., 14, 1969, no.5, 673-691.