Abstract
This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in \(L_p\) spaces and in weighted \(L_p\) spaces (1≤p<∞). Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness.
Authors
Octavian Agratini
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Ali Aral
Kirikkale University, Turkey
Keywords
Landau operator; weighted space; Korovkin theorem, modulus of smoothness
requires subscription: https://doi.org/10.1007/s00025-020-01319-9
Cite this paper as:
O. Agratini, A. Aral, Approximation of some classes of functions by Landau type operators, Results in Mathematics, 76 (2021) art. no. 12, https://doi.org/10.1007/s00025-020-01319-9
About this paper
Print ISSN
1422-6383
Online ISSN
1420-9012
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