Ergodic properties of random infinite products of nonexpansive mappings

• Autorzy: Reich S. , Zaslavski A. J.

Identyfikatory

DOI

10.7862/rf.2017.10

• Języki publikacji: EN

Abstrakty

EN

In this paper we are concerned with the asymptotic behavior of random (unrestricted) infinite products of nonexpansive selfmappings of closed and convex subsets of a complete hyperbolic space. In contrast with our previous work in this direction, we no longer assume that these subsets are bounded. We first establish two theorems regarding the stability of the random weak ergodic property and then prove a related generic result. These results also extend our recent investigations regarding nonrandom infinite products.

Słowa kluczowe

EN

complete metric space; hyperbolic space; infinite product; nonexpansive mapping; random weak ergodic property

PL

przestrzeń metryczna pełna; przestrzeń hiperboliczna; produkt nieskończony; mapowanie; własności ergodyczne

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2017
• Tom: Vol. 40
• Strony: 149--159
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Reich S.

• Department of Mathematics, The Technion - Israel Institute of Technology, 32000 Haifa, Israel

autor

Zaslavski A. J.

• Department of Mathematics, The Technion - Israel Institute of Technology, 32000 Haifa, Israel

Bibliografia

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• [2] H.H. Bauschke, J.M. Borwein and A.S. Lewis, The method of cyclic projections for closed convex sets in Hilbert space, Recent Developments in Optimization Theory and Nonlinear Analysis, Contemporary Mathematics 204 (1997) 1-38.
• [3] Y. Censor, S. Reich, Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization, Optimization 37 (1996) 323-339.
• [4] J.E. Cohen, Ergodic theorems in demography, Bull. Amer. Math. Soc. 1 (1979) 275-295.
• [5] J. Dye, S. Reich, Random products of nonexpansive mappings, Optimization and Nonlinear Analysis, Pitman Research Notes in Mathematics Series 244 (1992) 106-118.
• [6] K. Goebel, S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York and Basel 1984.
• [7] S. Reich, The alternating algorithm of von Neumann in the Hilbert ball, Dynamic Systems Appl. 2 (1993) 21-25.
• [8] S. Reich, I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Analysis 15 (1990) 537-558.
• [9] S. Reich, A.J. Zaslavski, Convergence of generic infinite products of nonexpansive and uniformly continuous operators, Nonlinear Analysis 36 (1999) 1049-1065.
• [10] S. Reich, A.J. Zaslavski, Generic aspects of metric fixed point theory, Handbook of Metric Fixed Point Theory, Kluwer, Dordrecht 2001 557-575.
• [11] S. Reich, A.J. Zaslavski, Genericity in Nonlinear Analysis, Developments in Mathematics 34, Springer, New York 2014.
• [12] S. Reich, A.J. Zaslavski, Asymptotic behavior of infinite products of nonexpansive mappings, J. Nonlinear Convex. Anal. 17 (2016) 1967-1973.
• [13] S. Reich and A.J. Zaslavski, Asymptotic behavior of generic infinite products of nonexpansive mappings, J. Nonlinear Convex Anal. 18 (2017) 17-27.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).