Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings

• Main Authors: Bunyawat,A., Suantai,S.
• Format: Article
• Published: Springer Publishing Company 2015
• Subjects: Geometry and Topology; Applied Mathematics
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84902585998&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38741
• Institution: Chiang Mai University

A new general iterative method for finding a common element of the set of solutions of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and studied. A strong convergence theorem of the proposed iterative scheme to a common fixed point of a countable family of nonexpansive mappings and a solution of variational inequality of an inverse strongly monotone mapping are established. Moreover, we apply our main result to obtain strong convergence theorems for a countable family of nonexpansive mappings and a strictly pseudocontractive mapping, and a countable family of uniformly k-strictly pseudocontractive mappings and an inverse strongly monotone mapping. Our main results improve and extend the corresponding result obtained by Klin-eam and Suantai (J Inequal Appl 520301, 16 pp, 2009). © 2011 Bunyawat and Suantai; licensee Springer.