Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

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

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

Sehie Park (1996)

Commentationes Mathematicae Universitatis Carolinae

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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

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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 periodic and firmly lipschitzian mappings in Banach spaces

Krzysztof Pupka (2012)

Commentationes Mathematicae Universitatis Carolinae

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W.A. Kirk in 1971 showed that if $T : C \to C$ , where $C$ is a closed and convex subset of a Banach space, is $n$ -periodic and uniformly $k$ -lipschitzian mapping with $k < k_{0} (n)$ , then $T$ has a fixed point. This result implies estimates of $k_{0} (n)$ for natural $n \geq 2$ for the general class of $k$ -lipschitzian mappings. In these cases, $k_{0} (n)$ are less than or equal to 2. Using very simple method we extend this and later results for a certain subclass of the family of $k$ -lipschitzian mappings. In the paper we show that $k_{0} (3) > 2$ in any Banach...

Remarks on fixed points of rotative Lipschitzian mappings

Jarosław Górnicki (1999)

Commentationes Mathematicae Universitatis Carolinae

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Let $C$ be a nonempty closed convex subset of a Banach space $E$ and $T : C \to C$ a $k$ -Lipschitzian rotative mapping, i.eṡuch that $∥ T x - T y ∥ \leq k \cdot ∥ x - y ∥$ and $∥ T^{n} x - x ∥ \leq a \cdot ∥ x - T x ∥$ for some real $k$ , $a$ and an integer $n > a$ . The paper concerns the existence of a fixed point of $T$ in $p$ -uniformly convex Banach spaces, depending on $k$ , $a$ and $n = 2, 3$ .