A fixed point theorem in non-Archimedean vector spaces
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- by C. Petalas and T. Vidalis PDF
- Proc. Amer. Math. Soc. 118 (1993), 819-821 Request permission
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 $X, ||Tx - Ty|| < ||x - y||\;(||Tx - Ty|| \leqslant ||x - y||)$. In this paper we prove that every contractive mapping on a spherically complete non-Archimedean normed space has a unique fixed point.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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