A fixed point theorem for local pseudo-contractions in uniformly convex spaces |
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Authors: | W. A. Kirk |
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Affiliation: | (1) Department of Mathematics, The University of Iowa, 52242 Iowa City, Iowa, USA |
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Abstract: | It is proved that if D is a bounded open subset of a uniformly convex Banach space X and is a continuous mapping which is a local pseudo-contraction (e.g., locally nonexpansive) on D, then T has a fixed point in D if there exists xD such that z–Tz<x–Tx for all x in the boundary of D. |
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