Algorithms for Hammerstein inclusions in certain Banach spaces
Volume 12, Issue 6, pp 387--404
http://dx.doi.org/10.22436/jnsa.012.06.05
Publication Date: February 04, 2019
Submission Date: March 10, 2018
Revision Date: November 19, 2018
Accteptance Date: December 01, 2018
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Authors
Moustapha Sene
- Gaston Berger University, Saint Louis, Senegal.
Mariama Ndiaye
- Gaston Berger University, Saint Louis, Senegal.
Ngalla Djitte
- Gaston Berger University, Saint Louis, Senegal.
Abstract
Let \(E\) be a reflexive smooth and strictly convex real Banach space. Let \(F: E\rightarrow 2^{E^*}\) and \(K: E^*\rightarrow E\) be bounded maximal monotone mappings such that \(D(F)=E\) and \(R(F)=D(K)=E^*\). Suppose that the Hammerstein inclusion \(0\in u+KFu \) has a solution in \(E\). We present in this paper a new algorithm for approximating solutions of the inclusion \(0\in u+KFu \).
Then we prove strong convergence theorems. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings. Furthermore,
our technique of proof is of independent interest.
Share and Cite
ISRP Style
Moustapha Sene, Mariama Ndiaye, Ngalla Djitte, Algorithms for Hammerstein inclusions in certain Banach spaces, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 6, 387--404
AMA Style
Sene Moustapha, Ndiaye Mariama, Djitte Ngalla, Algorithms for Hammerstein inclusions in certain Banach spaces. J. Nonlinear Sci. Appl. (2019); 12(6):387--404
Chicago/Turabian Style
Sene, Moustapha, Ndiaye, Mariama, Djitte, Ngalla. "Algorithms for Hammerstein inclusions in certain Banach spaces." Journal of Nonlinear Sciences and Applications, 12, no. 6 (2019): 387--404
Keywords
- Hammerstein equation
- monotone
- iterative algorithm
MSC
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