The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems
In this paper we study a class of operator equations A(x, x) + B(x, x) = x in ordered Banach spaces, where A, B are two mixed monotone operators. Various theorems are established to guarantee the existence of a unique solution to the problem. In addition, associated iterative schemes have been estab...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Shomal University
2016
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| Online Access: | http://www.tjnsa.com/includes/files/articles/Vol9_Iss5_2943--2958_The_unique_solution_of_a_class_of.pdf http://hdl.handle.net/20.500.11937/39057 |
| _version_ | 1848755487114264576 |
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| author | Liu, Lishan Zhang, X. Jiang, J. Wu, Yong Hong |
| author_facet | Liu, Lishan Zhang, X. Jiang, J. Wu, Yong Hong |
| author_sort | Liu, Lishan |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper we study a class of operator equations A(x, x) + B(x, x) = x in ordered Banach spaces, where A, B are two mixed monotone operators. Various theorems are established to guarantee the existence of a unique solution to the problem. In addition, associated iterative schemes have been established for finding the approximate solution converging to the fixed point of the problem. We also study the solution of the nonlinear eigenvalue equation A(x, x) + B(x, x) = λx and discuss its dependency to the parameter. Our results extend and improve many known results in this field of study. We have also successfully demonstrated the application of our results to the study of nonlinear fractional differential equations with two-point boundary conditions. |
| first_indexed | 2025-11-14T08:57:05Z |
| format | Journal Article |
| id | curtin-20.500.11937-39057 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:57:05Z |
| publishDate | 2016 |
| publisher | Shomal University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-390572017-01-30T14:29:50Z The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems Liu, Lishan Zhang, X. Jiang, J. Wu, Yong Hong In this paper we study a class of operator equations A(x, x) + B(x, x) = x in ordered Banach spaces, where A, B are two mixed monotone operators. Various theorems are established to guarantee the existence of a unique solution to the problem. In addition, associated iterative schemes have been established for finding the approximate solution converging to the fixed point of the problem. We also study the solution of the nonlinear eigenvalue equation A(x, x) + B(x, x) = λx and discuss its dependency to the parameter. Our results extend and improve many known results in this field of study. We have also successfully demonstrated the application of our results to the study of nonlinear fractional differential equations with two-point boundary conditions. 2016 Journal Article http://hdl.handle.net/20.500.11937/39057 http://www.tjnsa.com/includes/files/articles/Vol9_Iss5_2943--2958_The_unique_solution_of_a_class_of.pdf Shomal University restricted |
| spellingShingle | Liu, Lishan Zhang, X. Jiang, J. Wu, Yong Hong The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| title | The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| title_full | The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| title_fullStr | The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| title_full_unstemmed | The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| title_short | The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| title_sort | unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems |
| url | http://www.tjnsa.com/includes/files/articles/Vol9_Iss5_2943--2958_The_unique_solution_of_a_class_of.pdf http://hdl.handle.net/20.500.11937/39057 |