Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A fixed point theorem in non-Archimedean vector spaces


Authors: C. Petalas and T. Vidalis
Journal: Proc. Amer. Math. Soc. 118 (1993), 819-821
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1993-1132421-2
MathSciNet review: 1132421
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A mapping $ T$ defined on a normed linear space $ X$ and taking values in $ X$ is said to be contractive (nonexpansive) if whenever $ x$ and $ y$ are distinct points in $ X,\,\vert\vert Tx - Ty\vert\vert < \vert\vert x - y\vert\vert\;(\vert\vert Tx - Ty\vert\vert \leqslant \vert\vert x - y\vert\vert)$. In this paper we prove that every contractive mapping on a spherically complete non-Archimedean normed space has a unique fixed point.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H25

Retrieve articles in all journals with MSC: 54H25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1132421-2
Keywords: Fixed point, non-Archimedean vector space
Article copyright: © Copyright 1993 American Mathematical Society