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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 196, Issue 4, pp 1441–1458 | Cite as

A note on a fixed point theorem on topological cylinders

  • Guglielmo FeltrinEmail author
Article
  • 218 Downloads

Abstract

We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skiĭ ones.

Keywords

Fixed point theorems Fixed point index Brouwer fixed point theorem Schauder fixed point theorem Krasnosel’skiĭ fixed point theorem in cones 

Mathematics Subject Classification

47H10 37C25 47H11 54H25 

Notes

Acknowledgements

This work benefited from long enlightening discussions, helpful suggestions and encouragement of Professor Fabio Zanolin. This research was supported by SISSA - International School for Advanced Studies and Università degli Studi di Udine.

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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.SISSA - International School for Advanced StudiesTriesteItaly

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