A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems
We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and stric...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2011-01-01
|
Series: | International Journal of Mathematics and Mathematical Sciences |
Online Access: | http://dx.doi.org/10.1155/2011/131890 |
id |
doaj-1a6da89267c44daf9ec5888775d411d0 |
---|---|
record_format |
Article |
spelling |
doaj-1a6da89267c44daf9ec5888775d411d02020-11-24T21:35:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/131890131890A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium ProblemsYekini Shehu0Mathematics Institute, African University of Science and Technology, Abuja, NigeriaWe construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.http://dx.doi.org/10.1155/2011/131890 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yekini Shehu |
spellingShingle |
Yekini Shehu A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems International Journal of Mathematics and Mathematical Sciences |
author_facet |
Yekini Shehu |
author_sort |
Yekini Shehu |
title |
A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
title_short |
A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
title_full |
A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
title_fullStr |
A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
title_full_unstemmed |
A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems |
title_sort |
new hybrid iterative scheme for countable families of relatively quasi-nonexpansive mappings and system of equilibrium problems |
publisher |
Hindawi Limited |
series |
International Journal of Mathematics and Mathematical Sciences |
issn |
0161-1712 1687-0425 |
publishDate |
2011-01-01 |
description |
We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth
and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature. |
url |
http://dx.doi.org/10.1155/2011/131890 |
work_keys_str_mv |
AT yekinishehu anewhybriditerativeschemeforcountablefamiliesofrelativelyquasinonexpansivemappingsandsystemofequilibriumproblems AT yekinishehu newhybriditerativeschemeforcountablefamiliesofrelativelyquasinonexpansivemappingsandsystemofequilibriumproblems |
_version_ |
1725943594623172608 |