Abstract
A very general multivariate positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized Shilkret operators are presented fulfilling all the above properties, the higher order of multivariate approximation of these operators is also considered. It follows [3].
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References
G.A. Anastassiou, High order approximation by multivariate shift-invariant convolution type operators, in Computers and Mathematics with Applications, ed. by G.A. Anastassiou. Special issue on Computational Methods in Analysis, vol. 48 (2004), pp. 1245–1261
G.A. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)
G.A. Anastassiou, Approximation by shift invariant multivariate sublinear-Shilkret operators (2018). Submitted
G.A. Anastassiou, H.H. Gonska, On some shift invariant integral operators, multivariate case, in Proceedings of International Conference on Approximation, Probability, and Related Fields, U.C.S.B., Santa Barbara, CA, 20–22 May 1993, ed. G.A. Anastassiou, S.T. Rachev (Plenum Press, New York, 1993), pp. 41–64
G.A. Anastassiou, S. Gal, Approximation Theory (Birkhauser, Boston, 2000)
N. Shilkret, Maxitive measure and integration. Indag. Math. 33, 109–116 (1971)
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Anastassiou, G.A. (2019). Quantitative Approximation by Shift Invariant Multivariate Sublinear-Shilkret Operators. In: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Studies in Systems, Decision and Control, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-030-04287-5_14
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DOI: https://doi.org/10.1007/978-3-030-04287-5_14
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