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Fixed points for k mappings on a complete metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

2011

Vol. 44, nr 2

349--357

A fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [1] from two mappings to three map pings, and after that, a generalization for an arbitrary number of mappings is obtained. As corollaries of these results we obtain the extending of Theorems of Nesic, Rhoades, Chatterjea, Rus and Kannan for an arbitrary number of mappings.

Asymptotic behavior of relatively nonexpansive operators in Banach spaces

Butnariu D., Reich S., Zaslavski A. J.

Journal of Applied Analysis

2001

Vol. 7, nr 2

151-174

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.