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

• Main Authors: Suantai Suthep, Bunyawat Aunyarat
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Subjects: countable family of nonexpansive mappings; variational inequality; inverse strongly monotone mapping; strictly pseudocontractive mapping; countable family of uniformly <it>k</it>-strictly pseudocontractive mappings
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/1/47

<p>Abstract</p> <p>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 <it>k</it>-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).</p> <p><b>Mathematics Subject Classification (2000): </b>47H09, 47H10</p>