A noncompactness measure for tvs-metric cone spaces and some applications

Volume 9, Issue 5, pp 2680--2687 http://dx.doi.org/10.22436/jnsa.009.05.64

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Authors

Raúl Fierro - Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile.

Abstract

We provide a natural topology for a cone metric space and a noncompactness measure is deffned for this space, which enables us to extend existing results for mappings and set-valued mappings defined on classical metric spaces. Moreover it is proved that the topology of any uniform topological space is generated by a cone metric.

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Keywords

• Approximate and fixed points
• noncompactness measure
• uniform spaces
• set-valued mapping
• tvs-cone metric space.

MSC

•  46A50
•  47H10
•  47H04

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