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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.

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

  • [1] D. E. Alspach, A fixed point free nonexpansive mapping, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR 612733 (82j:47070)
  • [2] J. B. Baillon and R. Schöneberg, Asymptotic normal structure and fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 81 (1981), 257-264. MR 593469 (82c:47068)
  • [3] W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004-1006. MR 0189009 (32:6436)
  • [4] A. C M. van Rooij, Non-Archimedean functional analysis, Marcel Dekker, New York, 1978. MR 512894 (81a:46084)

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

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