Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Paolamaria Pietramala

Displaying similar documents to “Convergence of approximating fixed points sets for multivalued nonexpansive mappings”

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 $L^{2} (Ω)$ .

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.

Another fixed point theorem for nonexpansive potential operators

Biagio Ricceri (2012)

Studia Mathematica

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We prove the following result: Let X be a real Hilbert space and let J: X → ℝ be a C¹ functional with a nonexpansive derivative. Then, for each r > 0, the following alternative holds: either J’ has a fixed point with norm less than r, or $s u p_{| | x | | = r} J (x) = s u p_{{| | u | |}_{L ² ([0, 1], X)} = r} \int_{0}^{1} J (u (t)) d t$ .

Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces

Claudio H. Morales (1992)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a real Banach space. A multivalued operator $T$ from $K$ into $2^{X}$ is said to be pseudo-contractive if for every $x, y$ in $K$ , $u \in T (x)$ , $v \in T (y)$ and all $r > 0$ , $∥ x - y ∥ \leq ∥ (1 + r) (x - y) - r (u - v) ∥$ . Denote by $G (z, w)$ the set ${u \in K : ∥ u - w ∥ \leq ∥ u - z ∥}$ . Suppose every bounded closed and convex subset of $X$ has the fixed point property with respect to nonexpansive selfmappings. Now if $T$ is a Lipschitzian and pseudo-contractive mapping from $K$ into the family of closed and bounded subsets of $K$ so that the set $G (z, w)$ is bounded for some $z \in K$ and some $w \in T (z)$ , then $T$ has a fixed point in $K$ . ...