Remarks on fixed points of rotative Lipschitzian mappings

Jarosław Górnicki

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.

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On Diviccaro, Fisher and Sessa open questions

On a generalization of a Greguš fixed point theorem