Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.
Bibliographical noteFunding Information:
The work of the first two authors was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Grants 293/97 and 592/00). The second author was also partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund — E. and M. Mendelson Research Fund.
- Bregman distance
- Convex function
- Fixed point
- Generic property
- Iterative algorithm
- Uniform space
ASJC Scopus subject areas
- Mathematical Physics
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics
- Applied Mathematics