Approximation methods for nonlinear operator equations

Authors:
C. E. Chidume and H. Zegeye

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2467-2478

MSC (2000):
Primary 47H04, 47H06, 47H30, 47J05, 47J25

DOI:
https://doi.org/10.1090/S0002-9939-02-06769-2

Published electronically:
November 13, 2002

MathSciNet review:
1974645

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a real normed linear space and be a uniformly quasi-accretive map. For arbitrary define the sequence by where is a positve real sequence satisfying the following conditions: (i) ; (ii) . For , assume that and that , where (the set of all positive integers): and is a strictly increasing function with . It is proved that a Mann-type iteration process converges strongly to . Furthermore if, in addition, is a uniformly continuous map, it is proved, without the condition on , that the Mann-type iteration process converges strongly to . As a consequence, corresponding convergence theorems for fixed points of hemi-contractive maps are proved.

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Additional Information

**C. E. Chidume**

Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Email:
chidume@ictp.trieste.it

**H. Zegeye**

Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Email:
habz@ictp.trieste.it

DOI:
https://doi.org/10.1090/S0002-9939-02-06769-2

Keywords:
Bounded operators,
nonexpansive retraction,
uniformly accretive maps,
uniformly pseudocontractive maps,
uniformly smooth Banach spaces

Received by editor(s):
December 8, 2001

Received by editor(s) in revised form:
March 18, 2002

Published electronically:
November 13, 2002

Additional Notes:
The second author undertook this work with the support of the “ICTP Programme for Training and Research in Italian Laboratories, Trieste, Italy".

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2002
American Mathematical Society