Duality Fixed Point and Zero Point Theorems and Applications
The following main results have been given. (1) Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1)-L-Lipschitz mapping with condition 0<(pL/c2)1/(p-1)<1. Then T has a unique generalized duality fixed point x*∈E and (2) let E be a p-uniformly convex Banach space and let T:E→E*...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/391301 |
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| _version_ | 1849304845479051264 |
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| author | Qingqing Cheng Yongfu Su Jingling Zhang |
| author_facet | Qingqing Cheng Yongfu Su Jingling Zhang |
| author_sort | Qingqing Cheng |
| collection | DOAJ |
| description | The following main results have been given. (1) Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1)-L-Lipschitz mapping with condition 0<(pL/c2)1/(p-1)<1. Then T has a unique generalized duality fixed point x*∈E and (2) let E be a p-uniformly convex Banach space and let T:E→E* be a q-α-inverse strongly monotone mapping with conditions 1/p+1/q=1, 0<(q/(q-1)c2)q-1<α. Then T has a unique generalized duality fixed point x*∈E. (3) Let E be a 2-uniformly smooth and uniformly convex Banach space with uniformly convex constant c and uniformly smooth constant b and let T:E→E* be a L-lipschitz mapping with condition 0<2b/c2<1. Then T has a unique zero point x*. These main results can be used for solving the relative variational inequalities and optimal problems and operator equations. |
| format | Article |
| id | doaj-art-3fbbd8e5f1c341efae87ffecb555f78e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3fbbd8e5f1c341efae87ffecb555f78e2025-08-20T03:55:36ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/391301391301Duality Fixed Point and Zero Point Theorems and ApplicationsQingqing Cheng0Yongfu Su1Jingling Zhang2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaThe following main results have been given. (1) Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1)-L-Lipschitz mapping with condition 0<(pL/c2)1/(p-1)<1. Then T has a unique generalized duality fixed point x*∈E and (2) let E be a p-uniformly convex Banach space and let T:E→E* be a q-α-inverse strongly monotone mapping with conditions 1/p+1/q=1, 0<(q/(q-1)c2)q-1<α. Then T has a unique generalized duality fixed point x*∈E. (3) Let E be a 2-uniformly smooth and uniformly convex Banach space with uniformly convex constant c and uniformly smooth constant b and let T:E→E* be a L-lipschitz mapping with condition 0<2b/c2<1. Then T has a unique zero point x*. These main results can be used for solving the relative variational inequalities and optimal problems and operator equations.http://dx.doi.org/10.1155/2012/391301 |
| spellingShingle | Qingqing Cheng Yongfu Su Jingling Zhang Duality Fixed Point and Zero Point Theorems and Applications Abstract and Applied Analysis |
| title | Duality Fixed Point and Zero Point Theorems and Applications |
| title_full | Duality Fixed Point and Zero Point Theorems and Applications |
| title_fullStr | Duality Fixed Point and Zero Point Theorems and Applications |
| title_full_unstemmed | Duality Fixed Point and Zero Point Theorems and Applications |
| title_short | Duality Fixed Point and Zero Point Theorems and Applications |
| title_sort | duality fixed point and zero point theorems and applications |
| url | http://dx.doi.org/10.1155/2012/391301 |
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