On Diviccaro, Fisher and Sessa open questions

Ljubomir B. Ćirić

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

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.

Some cohomological aspects of the Banach fixed point principle

Ludvík Janoš (2011)

Mathematica Bohemica

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Let $T : X \to X$ be a continuous selfmap of a compact metrizable space $X$ . We prove the equivalence of the following two statements: (1) The mapping $T$ is a Banach contraction relative to some compatible metric on $X$ . (2) There is a countable point separating family $ℱ \subset 𝒞 (X)$ of non-negative functions $f \in 𝒞 (X)$ such that for every $f \in ℱ$ there is $g \in 𝒞 (X)$ with $f = g - g \circ T$ .

The conjugate of a product of linear relations

Jacob J. Jaftha (2006)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ , $Y$ and $Z$ be normed linear spaces with $T (X \to Y)$ and $S (Y \to Z)$ linear relations, i.e. setvalued maps. We seek necessary and sufficient conditions that would ensure that ${(S T)}^{'} = T^{'} S^{'}$ . First, we cast the concepts of relative boundedness and co-continuity in the set valued case and establish a duality. This duality turns out to be similar to the one that exists for densely defined linear operators and is then used to establish the necessary and sufficient conditions. These conditions are similar to those for...