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http://hdl.handle.net/11129/3438
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Title: | New Korovkin Type Theorem for Non-Tensor Meyer–König and Zeller Operators |
Authors: | Özarslan, Mehmet Ali Eastern Mediterranean University, Faculty of Arts & Sciences, Department of Mathematics |
Keywords: | positive linear operators, Meyer–König and Zeller operators, 41A36, Korovkin type theorem generating function, 41A25, modulus of continuity, Mathematics, general, Mathematics |
Issue Date: | 2016 |
Publisher: | Springer International Publishing |
Abstract: | In this paper, we introduce a certain class of linear positive operators via a generating function, which includes the non-tensor MKZ operators and their non-trivial extension. In investigating the approximation properties, we prove a new Korovkin type approximation theorem by using appropriate test functions. We compute the rate of convergence of these operators by means of the modulus of continuity and the elements of modified Lipschitz class functions. Furthermore, we give functional partial differential equations for this class. Using the corresponding equations, we calculate the first few moments of the non-tensor MKZ operators and investigate their approximation properties. Finally, we state the multivariate versions of the results and obtain the convergence properties of the multivariate Meyer–König and Zeller operators. |
URI: | http://dx.doi.org/10.1007/s00025-015-0472-0 http://hdl.handle.net/11129/3438 |
ISSN: | 1422-6383 (print) 1420-9012(online) |
Appears in Collections: | MAT – Journal Articles: Publisher & Author Versions (Post-Print Author Versions) – Mathematics
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