Remarks on fixed points of rotative Lipschitzian mappings

Jarosław Górnicki

Displaying similar documents to “Remarks on fixed points of rotative Lipschitzian mappings”

On Diviccaro, Fisher and Sessa open questions

Ljubomir B. Ćirić (1993)

Archivum Mathematicum

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Let $K$ be a closed convex subset of a complete convex metric space $X$ and $T, I : K \to K$ two compatible mappings satisfying following contraction definition: $T x, T y) \leq (I x, I y) + (1 - a) max {I x . T x), I y, T y)}$ for all $x, y$ in $K$ , where $0 < a < 1 / 2^{p - 1}$ and $p \geq 1$ . If $I$ is continuous and $I (K)$ contains $[T (K)]$ , then $T$ and $I$ have a unique common fixed point in $K$ and at this point $T$ is continuous. This result gives affirmative answers to open questions set forth by Diviccaro, Fisher and Sessa in connection with necessarity of hypotheses of linearity and non-expansivity of $I$ in their...

On a generalization of a Greguš fixed point theorem

Ljubomir B. Ćirić (2000)

Czechoslovak Mathematical Journal

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Let $C$ be a closed convex subset of a complete convex metric space $X$ . In this paper a class of selfmappings on $C$ , which satisfy the nonexpansive type condition $(2)$ below, is introduced and investigated. The main result is that such mappings have a unique fixed point.

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...

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 $L^{2} (Ω)$ .