Iterative approximation of solutions of nonlinear equations of Hammerstein type |
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Authors: | CE Chidume N Djitté |
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Institution: | 1. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy;2. Université Gaston Berger, Saint Louis, Sénégal |
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Abstract: | Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. |
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Keywords: | 47H04 47H06 47H15 47H17 47J25 |
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