Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang; Yu-Qing Chen; Yeol Je Cho; Byung-Soo Lee

On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces

Sehie Park (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $X$ be a uniformly convex Banach space, $D \subset X$ , $f : D \to X$ a nonexpansive map, and $K$ a closed bounded subset such that $\bar{co} K \subset D$ . If (1) ${f |}_{K}$ is weakly inward and $K$ is star-shaped or (2) ${f |}_{K}$ satisfies the Leray-Schauder boundary condition, then $f$ has a fixed point in $\bar{co} K$ . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Paolamaria Pietramala (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $K$ be a closed convex subset of a Hilbert space $H$ and $T : K ⊸ K$ a nonexpansive multivalued map with a unique fixed point $z$ such that ${z} = T (z)$ . It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to $z$ .

Displaying similar documents to “Fixed point theorems for nonexpansive operators with dissipative perturbations in cones”

On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces

Convergence of approximating fixed points sets for multivalued nonexpansive mappings