Geodesic
Strong Convergence Theorems for Nonexpansive Nonself-Mappings and Inverse-Strongly-Monotone Mappings
Journal of convex analysis, Tome 11 (2004) no. 1, pp. 069-08.

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We introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive nonself-mapping and the set of solutions of the variational inequality for an invererse-strongly-montone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of zeros of a maximal montone mapping and the set of zeros of an inverse-strongly-montone mapping and the problem of finding a common element of the closed convex set and the set of zeros of the gradient of a continuously Frechet differentiable convex functional.
Mots-clés : Metric projection, inverse-strongly-monotone mapping, nonexpansive nonself-mapping, variational inequality, strong convergence 
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     author = {H. Iiduka and W. Takahashi},
     title = {Strong {Convergence} {Theorems} for {Nonexpansive} {Nonself-Mappings} and {Inverse-Strongly-Monotone} {Mappings}},
     journal = {Journal of convex analysis},
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     number = {1},
     year = {2004},
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H. Iiduka; W. Takahashi. Strong Convergence Theorems for Nonexpansive Nonself-Mappings and Inverse-Strongly-Monotone Mappings. Journal of convex analysis, Tome 11 (2004) no. 1, pp. 069-08. http://geodesic.mathdoc.fr/item/JCA_2004_11_1_JCA_2004_11_1_a4/