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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 1
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Original Articles

An iterative algorithm for solving generalized variational inequality problems and fixed point problems

, &
Pages 209-225 | Received 03 Nov 2014, Accepted 18 Dec 2014, Published online: 14 Jan 2015
 

Abstract

We propose an iterative scheme for finding a common element of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem in Euclidean space . Under some mild conditions, we establish the convergence theorem for the proposed algorithm. We also give a suitable condition to ensure the intersection of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem to be nonempty. In addition, under certain error bound conditions, we prove the convergence rate of the iterative sequence. Preliminary computational experience is also reported.

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Funding

This work was supported by the National Natural Science Foundation of China [grant number 10671135]; the Key Project of Chinese Ministry of Education [grant number 212147]. The work of the third author was partially supported by the Grant NSC [grant number 103-2923-E-037-001-MY3].

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