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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
MathSciNet review: 1132421
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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.

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Keywords: Fixed point, non-Archimedean vector space
Article copyright: © Copyright 1993 American Mathematical Society

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