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- Title
Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type with Lipschitz and Bounded Nonlinear Operators.
- Authors
Djitte, N.; Sene, M.
- Abstract
Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm and F, K : E → E be Lipschitz accretive maps with D(K) = R(F) = E. Suppose that the Hammerstein equation u + KFu = 0 has a solution. An explicititeration method is shown to converge strongly to a solution of the equation. No invertibility assumption is imposed on Kand the operator F is not restricted to be angle-bounded. Our theorems are significant improvements on important recent results (e.g., Chiume and Djitte, 2012)).
- Subjects
APPROXIMATION theory; APPROXIMATE solutions (Logic); NUMERICAL solutions to nonlinear integral equations; HAMMERSTEIN equations; MATHEMATICAL bounds; NONLINEAR operators; BANACH spaces
- Publication
ISRN Applied Mathematics, 2012, p1
- ISSN
2090-5564
- Publication type
Article
- DOI
10.5402/2012/963802