Hybrid steepest-descent methods with a countable family of nonexpansive mappings for variational inequalities in Hilbert spaces

摘要

Let H be a Hilbert space and let and be the countable families of nonexpansive mappings of H into itself such that . Assume that F is a nonlinear operator which is κ-Lipschitzian and η-strong monotone on C. In this article, we devise a new iterative scheme {x _n } from an arbitrary initial point x ₀H for the countable family of nonexpansive mappings and and prove that {x _n } strongly converges to the unique solution x* of the variational inequality Applications to constrained generalized pseudoinverse are included.View full textDownload full textKeywordsnonexpansive mapping, Banach space, equilibrium problem, strong convergenceAMS Subject Classifications47H05, 47H09, 47J25, 47N10Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00036811.2011.559461