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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the approximation of fixed points for locally pseudo-contractive mappings
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by Claudio H. Morales and Simba A. Mutangadura PDF
Proc. Amer. Math. Soc. 123 (1995), 417-423 Request permission

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 $\left \| {z - Tz} \right \| < \left \| {x - Tx} \right \|$ 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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 417-423
  • MSC: Primary 47H09; Secondary 47H06, 47H10, 47H17
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1216820-8
  • MathSciNet review: 1216820