IJPAM: Volume 81, No. 2 (2012)

A FIXED POINT THEOREM FOR UNBOUNDED MAPS

Harry Gingold
Department of Mathematics
West Virginia University
Morgantown, WV 26506, USA


Abstract. A fixed point theorem is proven for unbounded maps in $\mathbb{R}^{n}$. The proof is aided by an unconventional compactification. Examples are provided.

Received: August 10, 2012

AMS Subject Classification: 47H10, 54H25

Key Words and Phrases: fixed point, map, contraction map, expansive, nonexpansive, unbounded, compactification, ideal set, ultra extended $\mathbb{R}^{n}$, $UE\mathbb{R}^{n}$, infinity, point at infinity, direction at infinity

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 2