Approximation of solutions of nonlinear equations of Hammerstein type in Hilbert space
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- by C. E. Chidume and H. Zegeye PDF
- Proc. Amer. Math. Soc. 133 (2005), 851-858 Request permission
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 $H$.References
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Additional Information
- C. E. Chidume
- Affiliation: The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
- MR Author ID: 232629
- Email: chidume@ictp.trieste.it
- H. Zegeye
- Affiliation: The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
- Email: habz@ictp.trieste.it
- 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
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 851-858
- MSC (2000): Primary 47H06, 47H15, 47H17, 47J25
- DOI: https://doi.org/10.1090/S0002-9939-04-07568-9
- MathSciNet review: 2113936