A generalization of Krasnosel'skii compression fixed point theorem by using star convex sets

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URI: http://hdl.handle.net/10347/31828
ISSN: 0308-2105
E-ISSN: 1473-7124
DOI: 10.1017/prm.2018.119

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2020

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Cambridge University Press
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Abstract

In the framework of fixed point theory, many generalizations of the classical results due to Krasnosel’skii are known. One of these extensions consists in relaxing the conditions imposed on the mapping, working with k-set contractions instead of continuous and compact maps. The aim of this work if to study in detail some fixed point results of this type, and obtain a certain generalization by using star convex sets.

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Krasnosel'skii fixed point theorem| k-set contraction| star convex set

Bibliographic citation

C. Lois-Prados, R. Rodríguez-López (2020). A generalization of Krasnosel'skii compression fixed point theorem by using star convex sets. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 150(1), 277–303.

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The research of C. Lois-Prados was partially supported by a grant of 'Programa de Iniciación á Investigacióon nas Ciencias Matemáticas e as súas Aplicacións' from the Vicerreitoría de Investigación e Innovación and the Instituto de Matemáticas (USC). The research of R. Rodríguez-López was partially supported by grant number MTM2016-75140-P (AEI/FEDER, UE).

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Copyright © Royal Society of Edinburgh 2019 Attribution-NonCommercial-NoDerivatives 4.0 Internacional

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Estatística, Análise Matemática e Optimización