Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
Let C be a nonempty bounded closed convex subset of a complete CAT(0) space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ d...
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/327434 |
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| author | P. Pasom B. Panyanak |
| author_facet | P. Pasom B. Panyanak |
| author_sort | P. Pasom |
| collection | DOAJ |
| description | Let C be a nonempty bounded closed convex subset of a complete CAT(0) space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmk)xk⊕tmkTmnky(m-1)k, y(m-1)k=(1-t(m-1)k)xk⊕t(m-1)kTm-1nky(m-2)k,y(m-2)k=(1-t(m-2)k)xk⊕t(m-2)kTm-2nky(m-3)k,…,y2k=(1-t2k)xk⊕t2kT2nky1k,y1k=(1-t1k)xk⊕t1kT1nky0k,y0k=xk, k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included. |
| format | Article |
| id | doaj-art-30ccb7edfbe947c483bce53401506e23 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-30ccb7edfbe947c483bce53401506e232025-02-03T05:58:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/327434327434Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach SpacesP. Pasom0B. Panyanak1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandLet C be a nonempty bounded closed convex subset of a complete CAT(0) space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmk)xk⊕tmkTmnky(m-1)k, y(m-1)k=(1-t(m-1)k)xk⊕t(m-1)kTm-1nky(m-2)k,y(m-2)k=(1-t(m-2)k)xk⊕t(m-2)kTm-2nky(m-3)k,…,y2k=(1-t2k)xk⊕t2kT2nky1k,y1k=(1-t1k)xk⊕t1kT1nky0k,y0k=xk, k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.http://dx.doi.org/10.1155/2012/327434 |
| spellingShingle | P. Pasom B. Panyanak Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces Journal of Applied Mathematics |
| title | Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces |
| title_full | Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces |
| title_fullStr | Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces |
| title_full_unstemmed | Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces |
| title_short | Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces |
| title_sort | common fixed points for asymptotic pointwise nonexpansive mappings in metric and banach spaces |
| url | http://dx.doi.org/10.1155/2012/327434 |
| work_keys_str_mv | AT ppasom commonfixedpointsforasymptoticpointwisenonexpansivemappingsinmetricandbanachspaces AT bpanyanak commonfixedpointsforasymptoticpointwisenonexpansivemappingsinmetricandbanachspaces |