The retractions onto the common fixed points of some families and semigroups of mappings

✍ Scribed by Shahram Saeidi

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 630 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.11.049

✦ Synopsis

Mapping of type (γ )

Nonexpansive mapping Retraction Weak limit a b s t r a c t Assume that C is a closed convex subset of a reflexive Banach space E and ϕ = {T i } i∈I is a family of self-mappings on C of type (γ ) such that F (ϕ), the common fixed point set of ϕ, is nonempty. From our results in this paper, it can be derived that:

, and every closed convex ϕ-invariant subset of C is R-invariant; the same result holds for a non-commutative right amenable semigroup ϕ, under some additional assumptions. Moreover, the existence of a (T i )-ergodic retraction R of type (γ )

for the family ϕ is discussed. We also apply some of our results to find ergodic retractions for nonexpansive affine mappings.