Convergence of paths for pseudo-contractive mappings in Banach spaces

Authors:
Claudio H. Morales and Jong Soo Jung

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3411-3419

MSC (1991):
Primary 47H10

DOI:
https://doi.org/10.1090/S0002-9939-00-05573-8

Published electronically:
May 18, 2000

MathSciNet review:
1707528

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let be a real Banach space, let be a closed convex subset of , and let , from into , be a pseudo-contractive mapping (i.e. for all and . Suppose the space has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of enjoys the Fixed Point Property for nonexpansive self-mappings. Then the path , , defined by the equation is continuous and strongly converges to a fixed point of as , provided that satisfies the weakly inward condition.

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Additional Information

**Claudio H. Morales**

Affiliation:
Department of Mathematics, University of Alabama, Huntsville, Alabama 35899

Email:
morales@math.uah.edu

**Jong Soo Jung**

Affiliation:
Department of Mathematics, Dong-A University, Pusan 604-714, Korea

Email:
jungjs@mail.donga.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-00-05573-8

Keywords:
Pseudo-contractive mappings,
uniformly Gâteaux differentiable norm.

Received by editor(s):
September 18, 1998

Received by editor(s) in revised form:
January 22, 1999

Published electronically:
May 18, 2000

Additional Notes:
This paper was carried out while the second author was visiting the University of Alabama in Huntsville under the financial support of the LG Yonam Foundation, 1998, and he would like to thank Professor Claudio H. Morales for his hospitality in the Department of Mathematics.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society