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Proceedings of the American Mathematical Society

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On the approximation of fixed points for locally pseudo-contractive mappings


Authors: Claudio H. Morales and Simba A. Mutangadura
Journal: Proc. Amer. Math. Soc. 123 (1995), 417-423
MSC: Primary 47H09; Secondary 47H06, 47H10, 47H17
MathSciNet review: 1216820
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Abstract: Let X and its dual $ {X^ \ast }$ be uniformly convex Banach spaces, D an open and bounded subset of X, T a continuous and pseudo-contractive mapping defined on $ {\text{cl}}(D)$ and taking values in X. If T satisfies the following condition: there exists $ z \in D$ such that $ \left\Vert {z - Tz} \right\Vert < \left\Vert {x - Tx} \right\Vert$ for all x on the boundary of D, then the trajectory $ t \to {z_t} \in D,t \in [0,1)$, defined by $ {z_t} = tT({z_t}) + (1 - t)z$ is continuous and converges strongly to a fixed point of T as $ t \to {1^ - }$.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1216820-8
Keywords: Pseudo-contractive mappings, uniform convexity
Article copyright: © Copyright 1995 American Mathematical Society