Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings
<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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
|
| Series: | Fixed Point Theory and Applications |
| Subjects: | |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/1/47 |
| Summary: | <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> |
|---|---|
| ISSN: | 1687-1820 1687-1812 |