A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings
Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/615107 |
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| author | C. E. Chidume E. U. Ofoedu |
| author_facet | C. E. Chidume E. U. Ofoedu |
| author_sort | C. E. Chidume |
| collection | DOAJ |
| description | Let E be a real Banach space, and K a closed convex nonempty subset of E.
Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings. A
simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient
conditions for this sequence to converge to a common fixed point of {Ti}i=1m are given. Furthermore, in the case that E is a uniformly convex real Banach space,
strong convergence of the sequence {xn}n=1∞ to a common fixed point of the family
{Ti}i=1m is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem. |
| format | Article |
| id | doaj-art-efea7adfd6524255bfec96d6b166b239 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-efea7adfd6524255bfec96d6b166b2392025-02-03T01:01:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/615107615107A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive MappingsC. E. Chidume0E. U. Ofoedu1The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, ItalyDepartment of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, NigeriaLet E be a real Banach space, and K a closed convex nonempty subset of E. Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i=1m are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence {xn}n=1∞ to a common fixed point of the family {Ti}i=1m is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.http://dx.doi.org/10.1155/2009/615107 |
| spellingShingle | C. E. Chidume E. U. Ofoedu A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings International Journal of Mathematics and Mathematical Sciences |
| title | A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings |
| title_full | A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings |
| title_fullStr | A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings |
| title_full_unstemmed | A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings |
| title_short | A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings |
| title_sort | new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2009/615107 |
| work_keys_str_mv | AT cechidume anewiterationprocessforapproximationofcommonfixedpointsforfinitefamiliesoftotalasymptoticallynonexpansivemappings AT euofoedu anewiterationprocessforapproximationofcommonfixedpointsforfinitefamiliesoftotalasymptoticallynonexpansivemappings AT cechidume newiterationprocessforapproximationofcommonfixedpointsforfinitefamiliesoftotalasymptoticallynonexpansivemappings AT euofoedu newiterationprocessforapproximationofcommonfixedpointsforfinitefamiliesoftotalasymptoticallynonexpansivemappings |