The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Poom Kumam; Somyot Plubtieng

Displaying similar documents to “The characteristic of noncompact convexity and random fixed point theorem for set-valued operators”

Random fixed point theorems for multivalued nonexpansive non-self-random operators.

Plubtieng, S., Kumam, P. (2006)

Journal of Applied Mathematics and Stochastic Analysis

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Random fixed points of multivalued inward random operators.

Khan, A.R., Domlo, A.A. (2006)

Journal of Applied Mathematics and Stochastic Analysis

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Random fixed point theorems for a certain class of mappings in Banach spaces

Jong Soo Jung, Yeol Je Cho, Shin Min Kang, Byung-Soo Lee, Balwant Singh Thakur (2000)

Czechoslovak Mathematical Journal

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Let $(Ω, Σ)$ be a measurable space and $C$ a nonempty bounded closed convex separable subset of $p$ -uniformly convex Banach space $E$ for some $p > 1$ . We prove random fixed point theorems for a class of mappings $T Ω \times C \to C$ satisfying: for each $x, y \in C$ , $ω \in Ω$ and integer $n \geq 1$ , $∥ T^{n} (ω, x) - T^{n} (ω, y) ∥ \leq a (ω) \cdot ∥ x - y ∥ + b (ω) {∥ x - T^{n} (ω, x) ∥ + ∥ y - T^{n} (ω, y) ∥} + c (ω) {∥ x - T^{n} (ω, y) ∥ + ∥ y - T^{n} (ω, x) ∥},$ where $a, b, c Ω \to [0, \infty)$ are functions satisfying certain conditions and $T^{n} (ω, x)$ is the value at $x$ of the $n$ -th iterate of the mapping $T (ω, \cdot)$ . Further we establish for these mappings some random fixed point theorems in a Hilbert space, in $L^{p}$ spaces, in Hardy spaces $H^{p}$ and in Sobolev...

Random fixed points for *-nonexpansive random operators.

Khan, Abdul Rahim, Hussain, Nawab (2001)

Journal of Applied Mathematics and Stochastic Analysis

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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.