A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems
A new modified Halpern-Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/632857 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849467868936142848 |
|---|---|
| author | Utith Inprasit Weerayuth Nilsrakoo |
| author_facet | Utith Inprasit Weerayuth Nilsrakoo |
| author_sort | Utith Inprasit |
| collection | DOAJ |
| description | A new modified Halpern-Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. The results presented in this work improve on the corresponding ones announced by many others. |
| format | Article |
| id | doaj-art-e112952b201d47208b1a0012f44f3816 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e112952b201d47208b1a0012f44f38162025-08-20T03:26:00ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/632857632857A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium ProblemsUtith Inprasit0Weerayuth Nilsrakoo1Department of Mathematics, Statistics, and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, ThailandDepartment of Mathematics, Statistics, and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, ThailandA new modified Halpern-Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. The results presented in this work improve on the corresponding ones announced by many others.http://dx.doi.org/10.1155/2011/632857 |
| spellingShingle | Utith Inprasit Weerayuth Nilsrakoo A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems Abstract and Applied Analysis |
| title | A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems |
| title_full | A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems |
| title_fullStr | A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems |
| title_full_unstemmed | A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems |
| title_short | A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems |
| title_sort | halpern mann type iteration for fixed point problems of a relatively nonexpansive mapping and a system of equilibrium problems |
| url | http://dx.doi.org/10.1155/2011/632857 |
| work_keys_str_mv | AT utithinprasit ahalpernmanntypeiterationforfixedpointproblemsofarelativelynonexpansivemappingandasystemofequilibriumproblems AT weerayuthnilsrakoo ahalpernmanntypeiterationforfixedpointproblemsofarelativelynonexpansivemappingandasystemofequilibriumproblems AT utithinprasit halpernmanntypeiterationforfixedpointproblemsofarelativelynonexpansivemappingandasystemofequilibriumproblems AT weerayuthnilsrakoo halpernmanntypeiterationforfixedpointproblemsofarelativelynonexpansivemappingandasystemofequilibriumproblems |