1. Approximation of zeros of inverse strongly monotone operators in Banach spaces
- Author
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Saejung, Satit and Yotkaew, Pongsakorn
- Subjects
- *
APPROXIMATION theory , *INVERSE problems , *MONOTONE operators , *BANACH spaces , *ALGORITHMS , *ITERATIVE methods (Mathematics) , *MATHEMATICAL sequences , *STOCHASTIC convergence , *VARIATIONAL inequalities (Mathematics) - Abstract
Abstract: In this paper, we consider the projection algorithm studied by Iiduka and Takahashi (2008) for finding a solution of the variational inequality problem for an inverse strongly monotone operator in a Banach space. We first remark that, under the assumptions imposed on the operator in their paper, the iterative sequence converges weakly to a zero of the operator, not just a solution of the variational inequality problem. In our proof, slightly modified from the original, we do not assume the uniform smoothness of a space as was the case there. Finally, using Halpern’s type method, we modify this algorithm to obtain the strong convergence to a zero of an inverse strongly monotone operator which is nearest to the initial element of the algorithm in the sense of the Bergman distance associated with the function . [Copyright &y& Elsevier]
- Published
- 2012
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