Warianty tytułu
Języki publikacji
Abstrakty
A very general multivariate positive sublinear Choquet 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 operators are presented fulfilling all the above properties; the higher order of multivariate approximation of these operators is also studied.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
115--126
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA, ganastss@memphis.edu
Bibliografia
- [1] G. A. Anastassiou, High order Approximation by multivariate shift-invariant convolution type operators, Comput. Math. Appl. 48 (2004), no. 9, 1245-1261.
- [2] G. A. Anastassiou, Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, 2011.
- [3] G. A. Anastassiou and S. Gal, Approximation Theory, Birkhäuser, Boston, 2000.
- [4] G. A. Anastassiou and H. H. Gonska, On some shift invariant integral operators, multivariate case, in: Approximation, Probability, and Related Fields (Santa Barbara 1993), Plenum Press, New York (1994), 41-64.
- [5] G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1954), 131-295.
- [6] D. Denneberg, Non-additive Measure and Integral, Kluwer, Dordrecht, 1994.
- [7] Z. Wang and G. J. Klir, Generalized Measure Theory, Springer, New York, 2009.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-20b12ac3-5aed-4502-a8fe-9126e595202f