研究了Banach空间的广义集值变分包含。首先指出了J U Jeong所著文章《Generalized set-valuedvariational inclusions and resolvent equations in Banach spaces》中的定理3.1是不成立的,然后借助预解算子技巧,建立了与广义变分包含...研究了Banach空间的广义集值变分包含。首先指出了J U Jeong所著文章《Generalized set-valuedvariational inclusions and resolvent equations in Banach spaces》中的定理3.1是不成立的,然后借助预解算子技巧,建立了与广义变分包含相关的迭代算法,并给出了广义变分包含的迭代收敛定理,从而更正了该定理。展开更多
In the paper under review,we consider the generation of fractional resolvent families by abstract differential operators.Our results can be simply incorporated in the study of corresponding abstract time-fractional eq...In the paper under review,we consider the generation of fractional resolvent families by abstract differential operators.Our results can be simply incorporated in the study of corresponding abstract time-fractional equations with Caputo fractional derivatives.展开更多
The purpose of this paper is to study the solution of 0∈ T（x） for an H- monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145（2003）795- 803] in Hilbert spaces, which is the first proposal of it...The purpose of this paper is to study the solution of 0∈ T（x） for an H- monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145（2003）795- 803] in Hilbert spaces, which is the first proposal of it＇s kind. Some strong and weak convergence results are presented and the relations between maximal monotone operators and H-monotone operators are analyzed. Simultaneously, we apply these results to the minimization problem for T = δf and provide some numerical examples to support the theoretical findings.展开更多
A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator tech...A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.展开更多
文摘研究了Banach空间的广义集值变分包含。首先指出了J U Jeong所著文章《Generalized set-valuedvariational inclusions and resolvent equations in Banach spaces》中的定理3.1是不成立的,然后借助预解算子技巧,建立了与广义变分包含相关的迭代算法,并给出了广义变分包含的迭代收敛定理,从而更正了该定理。
基金Supported by Ministry of Science and Technological Development,Republic of Serbia(Grant No.174024)
文摘In the paper under review,we consider the generation of fractional resolvent families by abstract differential operators.Our results can be simply incorporated in the study of corresponding abstract time-fractional equations with Caputo fractional derivatives.
基金supported by National Science Foundation of China(11071279)National Science Foundation for Young Scientists of China(11101320 and 61202178)+1 种基金the Fundamental Research Funds for the Central Universities(K5051370004K50511700007)
文摘The purpose of this paper is to study the solution of 0∈ T（x） for an H- monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145（2003）795- 803] in Hilbert spaces, which is the first proposal of it＇s kind. Some strong and weak convergence results are presented and the relations between maximal monotone operators and H-monotone operators are analyzed. Simultaneously, we apply these results to the minimization problem for T = δf and provide some numerical examples to support the theoretical findings.
基金Project supported by the Natural Science Foundation of Education Department of Sichuan Province ofChina (No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.
