Porosity and the bounded linear regularity property

• Autorzy: Reich S. , Zaslavski A. J.

Identyfikatory

DOI

10.1515/jaa-2014-0001

• Języki publikacji: EN

Abstrakty

EN

H. H. Bauschke and J. M. Borwein showed that in the space of all tuples of bounded, closed, and convex subsets of a Hilbert space with a nonempty intersection, a typical tuple has the bounded linear regularity property. This property is important because it leads to the convergence of infinite products of the corresponding nearest point projections to a point in the intersection. In the present paper we show that the subset of all tuples possessing the bounded linear regularity property has a porous complement. Moreover, our result is established in all normed spaces and for tuples of closed and convex sets, which are not necessarily bounded.

Słowa kluczowe

EN

bounded linear regularity; Hilbert space; normed space; porous set

PL

regularność; przestrzeń Hilberta; przestrzeń unormowana; zbiór porowaty

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2014
• Tom: Vol. 20, nr 1
• Strony: 1--6
• Opis fizyczny: Bibliogr. 8 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] F. S. De Blasi and J. Myjak, Sur la porosité de l’ensemble des contractions sans point fixe, C. R. Acad. Sci. Paris 308 (1989), 51-54.
• [3] F. S. De Blasi, J. Myjak, and P. L. Papini, Porous sets in best approximation theory, J. Lond. Math. Soc. 44 (1991), 135-142.
• [4] E. Pustylnik, S. Reich, and A. J. Zaslavski, Inner inclination of subspaces and infinite products of orthogonal projections, f. Non linear Convex Anal. 14 (2013), 423-436.
• [5] S. Reich and A. J. Zaslavski, Well-posedness and porosity in best approximation problems, Topol. Methods Nonlinear Anal. 18 (2001), 395-408.
• [6] S. Reich and A. J. Zaslavski, Generic existence of fixed points for set-valued mappings, Set-Valued Anal. 10 (2002), 287-296.
• [7] S. Reich and A. J. Zaslavski, Generic convergence of iterates for a class of nonlinear mappings, Fixed Point Theory Appl. 2004 (2004), 211-220.
• [8] A. J. Zaslavski, Optimization on Metric and Normed Spaces, Springer, New York, 2010.