On Diviccaro, Fisher and Sessa open questions

Ljubomir B. Ćirić

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 $n = 2, 3$ .

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.

Displaying similar documents to “On Diviccaro, Fisher and Sessa open questions”

Remarks on fixed points of rotative Lipschitzian mappings

On a generalization of a Greguš fixed point theorem