An iterative algorithm for solving generalized variational inequality problems and fixed point problems. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Tu, K.; Xia, F.Q.; Yao, J.C.
• Is Part Of: Applicable analysis. Volume 95:Issue 1(2016)
• Page Start: 209
• Page End: 225
• Publication Date: 2016-01-02
• Subjects: generalized variational inequality -- hyperplane -- Armijo-type linesearch -- nonexpansive mapping -- fixed point; 90C25 -- 49J40 -- 90C33; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2014.1002190
• Languages: English
• ISSNs: 0003-6811

Abstract

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.