Displaying similar documents to “Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces”

Fixed point theorems for set-valued Y-contractions

Ioan A. Rus, Adrian Petruşel, Gabriela Petruşel (2007)

Banach Center Publications

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The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.

Continuous dependence on parameters of the fixed points set for some set-valued operators

Eduard Kirr, Adrian Petruel (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.

Fixed point and continuation results for contractions in metric and gauge spaces

M. Frigon (2007)

Banach Center Publications

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We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.

Approximation of Univariate Set-Valued Functions - an Overview

Dyn, Nira, Farkhi, Elza, Mokhov, Alona (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65. The paper is an updated survey of our work on the approximation of univariate set-valued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact convex...

The Demyanov metric and some other metrics in the family of convex sets

Tadeusz Rzeżuchowski (2012)

Open Mathematics

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We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.

Continuous Selections in α-Convex Metric Spaces

F. S. De Blasi, G. Pianigiani (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.

Gluing Hyperconvex Metric Spaces

Benjamin Miesch (2015)

Analysis and Geometry in Metric Spaces

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We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.

Some Fixed Point Theorems for Kannan Mappings

Tejpal, Shavetambry, Narang, T. D. (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25. Some results on the existence and uniqueness of fixed points for Kannan mappings on admissible subsets of bounded metric spaces and on bounded closed convex subsets of complete convex metric spaces having uniform normal structure are proved in this paper. These results extend and generalize some results of Ismat Beg and Akbar Azam [Ind. J. Pure Appl. Math. 18 (1987), 594-596], A. A. Gillespie and B....