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

Sehie Park

Displaying similar documents to “On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces”

Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang, Yu-Qing Chen, Yeol Je Cho, Byung-Soo Lee (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let $P$ be a cone in a Hilbert space $H$ , $A : P \to 2^{P}$ be an accretive mapping (equivalently, $- A$ be a dissipative mapping) and $T : P \to P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $- A + T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^{2} (Ω)$ .

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Paolamaria Pietramala (1991)

Commentationes Mathematicae Universitatis Carolinae

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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 $z$ .

Fixed points of asymptotically regular mappings in spaces with uniformly normal structure

Jarosław Górnicki (1991)

Commentationes Mathematicae Universitatis Carolinae

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It is proved that: for every Banach space $X$ which has uniformly normal structure there exists a $k > 1$ with the property: if $A$ is a nonempty bounded closed convex subset of $X$ and $T : A \to A$ is an asymptotically regular mapping such that $\underset{n \to \infty}{lim inf} | | | T^{n} | | | < k,$ where $| | | T | | |$ is the Lipschitz constant (norm) of $T$ , then $T$ has a fixed point in $A$ .