Asymptotic behavior of resolvents of coaccretive operators in the Hilbert ball

0358114 - MÚ 2011 RIV GB eng J - Journal Article
Kopecká, Eva - Reich, S.
Asymptotic behavior of resolvents of coaccretive operators in the Hilbert ball.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 70, č. 9 (2009), s. 3187-3194. ISSN 0362-546X. E-ISSN 1873-5215
R&D Projects: GA ČR GA201/06/0018
Institutional research plan: CEZ:AV0Z10190503
Keywords : firmly nonexpansive mapping * Hilbert ball * hyperbolic metric
Subject RIV: BA - General Mathematics
Impact factor: 1.487, year: 2009

We study the resolvents of coaccretive operators in the Hilbert ball, with special emphasis on the asymptotic behavior of their compositions and metric convex combinations. We consider the case where the given coaccretive operators share a common fixed point inside the ball, as well as the case where they share a common sink point an its boundary. We establish weak convergence in the former case and strong convergence in the latter. We also present two related convergence results for a continuous implicit scheme.
Permanent Link: http://hdl.handle.net/11104/0196226