## 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