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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation of solutions of nonlinear equations of Hammerstein type in Hilbert space


Authors: C. E. Chidume and H. Zegeye
Journal: Proc. Amer. Math. Soc. 133 (2005), 851-858
MSC (2000): Primary 47H06, 47H15, 47H17, 47J25
Published electronically: September 29, 2004
MathSciNet review: 2113936
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Abstract: Let $H$ be a real Hilbert space. Let $F:D(F)\subseteq H\rightarrow H$, $K:D(K)\subseteq H\to H$ be bounded monotone mappings with $R(F)\subseteq D(K)$, where $D(F)$ and $D(K)$ are closed convex subsets of $H$ satisfying certain conditions. Suppose the equation $0=u+KFu$ has a solution in $D(F)$. Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on $K$, and the operators $K$ and $F$ need not be defined on compact subsets of $H$.


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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: http://dx.doi.org/10.1090/S0002-9939-04-07568-9
PII: S 0002-9939(04)07568-9
Keywords: Hilbert spaces, maximal monotone mappings, monotone mappings, range condition
Received by editor(s): October 8, 2003
Received by editor(s) in revised form: November 20, 2003
Published electronically: September 29, 2004
Additional Notes: The second author undertook this work when he was visiting the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, as a postdoctoral fellow.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.