Abstract
New iterative algorithm for variational inequality problem and fixed point problem in Hilbert spaces
Highlights
Let H be a Hilbert space and C be a nonempty closed convex subset of H
The variational inequality problem is denoted by V I(F, C) [5]
Very recently Zhou and Wang [23] simplified the algorithm of Buong and Duong and proved a strong convergence theorem for the variational inequality problem and fixed point problem on finite nonexpansive mappings in Hilbert space
Summary
Let H be a Hilbert space and C be a nonempty closed convex subset of H. In 2011, Buong and Duong [2] introduced a new iterative algorithm, based on a combination of thy hybrid steepest-descent method for variational inequalities with the Krasnosel’skii-Mann type algorithm for fixed point problems. Very recently Zhou and Wang [23] simplified the algorithm of Buong and Duong and proved a strong convergence theorem for the variational inequality problem and fixed point problem on finite nonexpansive mappings in Hilbert space. In this paper, motivated by the work of Zhou and Wang [23], we introduce a new iterative algorithm for solving the solution of variational inequality problem and prove the solution is the common fixed point of a countable family of nonexpansive mappings in Hilbert space
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