A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
Let X be a real uniformly convex Banach space and C a closed convex nonempty subset of X. Let {Ti}i=1r be a finite family of nonexpansive self-mappings of C. For a given x1∈C, let {xn} and {xn(i)}, i=1,2,…,r, be sequences defined xn(0)=xn,xn(1)=an1(1)T1xn(0)+(1-an1(1))xn(0),xn(2)=an2...
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| Format: | Article |
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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/10.1155/2009/391839 |
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| author | Suwicha Imnang Suthep Suantai |
| author_facet | Suwicha Imnang Suthep Suantai |
| author_sort | Suwicha Imnang |
| collection | DOAJ |
| description | Let X be a real uniformly convex Banach space and C a closed convex nonempty subset of X. Let {Ti}i=1r be a finite family of nonexpansive self-mappings of C. For a given x1∈C, let {xn} and {xn(i)}, i=1,2,…,r, be sequences defined
xn(0)=xn,xn(1)=an1(1)T1xn(0)+(1-an1(1))xn(0),xn(2)=an2(2)T2xn(1)+an1(2)T1xn+(1-an2(2)-an1(2))xn,…, xn+1=xn(r)=anr(r)Trxn(r-1)+an(r-1)(r)Tr-1xn(r-2)+⋯+an1(r)T1xn+(1-an(r)(r)-an(r-1)(r)-⋯-an1(r))xn,n≥1, where ani(j)∈[0,1] for all j∈{1,2,…,r}, n∈ℕ and i=1,2,…,j. In this paper, weak and strong convergence theorems of the sequence {xn} to a common fixed point of a finite family of nonexpansive mappings Ti (i=1,2,…,r) are established under some certain control conditions. |
| format | Article |
| id | doaj-art-8f177428b62842e3ade830190a47e97e |
| 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-8f177428b62842e3ade830190a47e97e2025-02-03T05:59:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/391839391839A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive MappingsSuwicha Imnang0Suthep Suantai1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, ThailandLet X be a real uniformly convex Banach space and C a closed convex nonempty subset of X. Let {Ti}i=1r be a finite family of nonexpansive self-mappings of C. For a given x1∈C, let {xn} and {xn(i)}, i=1,2,…,r, be sequences defined xn(0)=xn,xn(1)=an1(1)T1xn(0)+(1-an1(1))xn(0),xn(2)=an2(2)T2xn(1)+an1(2)T1xn+(1-an2(2)-an1(2))xn,…, xn+1=xn(r)=anr(r)Trxn(r-1)+an(r-1)(r)Tr-1xn(r-2)+⋯+an1(r)T1xn+(1-an(r)(r)-an(r-1)(r)-⋯-an1(r))xn,n≥1, where ani(j)∈[0,1] for all j∈{1,2,…,r}, n∈ℕ and i=1,2,…,j. In this paper, weak and strong convergence theorems of the sequence {xn} to a common fixed point of a finite family of nonexpansive mappings Ti (i=1,2,…,r) are established under some certain control conditions.http://dx.doi.org/10.1155/2009/391839 |
| spellingShingle | Suwicha Imnang Suthep Suantai A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings International Journal of Mathematics and Mathematical Sciences |
| title | A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings |
| title_full | A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings |
| title_fullStr | A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings |
| title_full_unstemmed | A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings |
| title_short | A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings |
| title_sort | new iterative method for common fixed points of a finite family of nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2009/391839 |
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