On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces
We establish the existence of a strong convergent selection of a modified Mann-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points F(T) of a multivalued (or single-valued) k-strictly pseudocontractive-type mapping T and the set of solutions EP(F) of an equi...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/7218487 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549071811772416 |
|---|---|
| author | F. O. Isiogugu P. Pillay P. U. Nwokoro |
| author_facet | F. O. Isiogugu P. Pillay P. U. Nwokoro |
| author_sort | F. O. Isiogugu |
| collection | DOAJ |
| description | We establish the existence of a strong convergent selection of a modified Mann-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points F(T) of a multivalued (or single-valued) k-strictly pseudocontractive-type mapping T and the set of solutions EP(F) of an equilibrium problem for a bifunction F in a real Hilbert space H. This work is a continuation of the study on the computability and applicability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of a sequence {Kn}n=1∞ of closed convex subsets of H from an arbitrary x0∈H and a sequence {xn}n=1∞ of the metric projections of x0 into Kn. The obtained result is a partial resolution of the controversy over the computability of such algorithms in the contemporary literature. |
| format | Article |
| id | doaj-art-0ca22629af7d4e16be06ad6c6fc3a934 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0ca22629af7d4e16be06ad6c6fc3a9342025-02-03T06:12:08ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/72184877218487On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert SpacesF. O. Isiogugu0P. Pillay1P. U. Nwokoro2School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Westville Campus, Durban 4000, South AfricaSchool of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Westville Campus, Durban 4000, South AfricaDepartment of Mathematics, University of Nigeria, Nsukka, NigeriaWe establish the existence of a strong convergent selection of a modified Mann-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points F(T) of a multivalued (or single-valued) k-strictly pseudocontractive-type mapping T and the set of solutions EP(F) of an equilibrium problem for a bifunction F in a real Hilbert space H. This work is a continuation of the study on the computability and applicability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of a sequence {Kn}n=1∞ of closed convex subsets of H from an arbitrary x0∈H and a sequence {xn}n=1∞ of the metric projections of x0 into Kn. The obtained result is a partial resolution of the controversy over the computability of such algorithms in the contemporary literature.http://dx.doi.org/10.1155/2018/7218487 |
| spellingShingle | F. O. Isiogugu P. Pillay P. U. Nwokoro On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces Abstract and Applied Analysis |
| title | On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces |
| title_full | On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces |
| title_fullStr | On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces |
| title_full_unstemmed | On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces |
| title_short | On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces |
| title_sort | on computability and applicability of mann reich sabach type algorithms for approximating the solutions of equilibrium problems in hilbert spaces |
| url | http://dx.doi.org/10.1155/2018/7218487 |
| work_keys_str_mv | AT foisiogugu oncomputabilityandapplicabilityofmannreichsabachtypealgorithmsforapproximatingthesolutionsofequilibriumproblemsinhilbertspaces AT ppillay oncomputabilityandapplicabilityofmannreichsabachtypealgorithmsforapproximatingthesolutionsofequilibriumproblemsinhilbertspaces AT punwokoro oncomputabilityandapplicabilityofmannreichsabachtypealgorithmsforapproximatingthesolutionsofequilibriumproblemsinhilbertspaces |