STRONG CONVERGENCE THEOREMS BY A HYBRID STEEPEST DESCENT METHOD FOR COUNTABLE NONEXPANSIVE MAPPINGS IN HILBERT SPACES

SHIGERU IEMOTO; WATARU TAKAHASHI

doi:10.32219/isms.69.2_227

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Keywords: variational inequality, hybrid steepest descent method, Hilbert space, strongly monotone, Lipschitzian, nonexpansive mapping

JOURNAL FREE ACCESS

2009 Volume 69 Issue 2 Pages 227-240

DOI https://doi.org/10.32219/isms.69.2_227

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Abstract

In this paper, we introduce a new iterative procedure for finding a solution of the variational inequality problem over the intersection of fixed point sets of infinite nonexpansive mappings in a Hilbert space and then discuss the strong convergence of the iterative procedure.

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