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Journal of Convex Analysis 11 (2004), No. 1, 069--080
Copyright Heldermann Verlag 2004
Strong Convergence Theorems for Nonexpansive Nonself-Mappings and Inverse-Strongly-Monotone Mappings
Hideaki Iiduka
Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology,
Oh-Okayama, Meguro-ku, Tokyo 152-8522, Japan,
Hideaki.Iiduka@is.titech.ac.jp
Wataru Takahashi
Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology,
Oh-Okayama, Meguro-ku, Tokyo 152-8522, Japan,
Wataru@is.titech.ac.jp
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.
Keywords: Metric projection, inverse-strongly-monotone mapping, nonexpansive nonself-mapping,
variational inequality, strong convergence.
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