Strong convergence theorem for approximation of solutions of equations of Hammerstein type

Let H be a real Hilbert space. Let K,F:H→H be bounded, continuous and monotone mappings. Suppose that u∗∈H is a solution to the Hammerstein equation u+KFu=0. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation. Further...

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Bibliographic Details
Published in:Nonlinear analysis 2012-09, Vol.75 (14), p.5664-5671
Main Authors: Chidume, C.E., Shehu, Y.
Format: Article
Language:English
Subjects:
Approximation
Construction
Convergence
Equations of Hammerstein type
Hilbert space
Hilbert spaces
Mapping
Mathematical analysis
Monotone operators
Nonlinearity
Strong convergence
Theorems
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Summary:Let H be a real Hilbert space. Let K,F:H→H be bounded, continuous and monotone mappings. Suppose that u∗∈H is a solution to the Hammerstein equation u+KFu=0. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation. Furthermore, we give some examples to show that our result is interdisciplinary in nature, covers a large variety of areas and should be of much interest to a wide audience.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.05.014