Approximate Solutions of Variational Inequalities on Sets of Common Fixed Points of a One-Parameter Semigroup of Nonexpansive Mappings
| Autor: | Jen-Chih Yao, S. Schaible, Lu-Chuan Ceng |
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| Rok vydání: | 2009 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Control and Optimization Semigroup Applied Mathematics Mathematical analysis Convex set Banach space Fixed-point theorem Management Science and Operations Research Fixed point Variational inequality Differentiable function Convex function Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 143:245-263 |
| ISSN: | 1573-2878 0022-3239 |
| DOI: | 10.1007/s10957-009-9581-9 |
| Popis: | Let \(\mathcal{T}\) be a one-parameter semigroup of nonexpansive mappings on a nonempty closed convex subset C of a strictly convex and reflexive Banach space X. Suppose additionally that X has a uniformly Gâteaux differentiable norm, C has normal structure, and \(\mathcal{T}\) has a common fixed point. Then it is proved that, under appropriate conditions on nonexpansive semigroups and iterative parameters, the approximate solutions obtained by the implicit and explicit viscosity iterative processes converge strongly to the same common fixed point of \(\mathcal{T}\), which is a solution of a certain variational inequality. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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