In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study ...In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.展开更多
In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the...In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the Painlev^-Kuratowski Convergence of the weak efficient solution sets and efficient solution sets for the perturbed vector equilibrium problems with a sequence of mappings converging in real linear metric spaces. These results extend and improve some known results in the literature.展开更多
In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequ...In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.展开更多
In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient soluti...In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painleve-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.展开更多
在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广...在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广和改进了相关文献(Attouch H,RiahiH.Stability results for Ekeland’s-variational principle and cone extremal solution;Huang X X.Stabilityin vector-valued and set-valued optimization)中的相应结果,并给出例子说明了所得结果的正确性。展开更多
文摘In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.
基金Supported by the National Natural Science Foundation of China(No.11301571.11271389.11271391)the Natural Science Foundation Project of ChongQing(No.CSTC,2012jjA00016.2011BA0030)the Education Committee Research Foundation of ChongQing(KJ130428)
文摘In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the Painlev^-Kuratowski Convergence of the weak efficient solution sets and efficient solution sets for the perturbed vector equilibrium problems with a sequence of mappings converging in real linear metric spaces. These results extend and improve some known results in the literature.
基金Supported by the National Natural Science Foundation of China (No. 10871216 and 11171362)
文摘In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.
基金Supported by the National Natural Science Foundation of China(No.11431004.11471059.11401058)the Basic and Advanced Research Project of Chongqing(cstc2017jcyj AX0382,cstc2015shmszx30004)+1 种基金the Program for University Innovation Team of Chongqing(CXTDX201601022)the Education Committee Project Foundation of Bayu Scholar
文摘In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painleve-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.
文摘在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广和改进了相关文献(Attouch H,RiahiH.Stability results for Ekeland’s-variational principle and cone extremal solution;Huang X X.Stabilityin vector-valued and set-valued optimization)中的相应结果,并给出例子说明了所得结果的正确性。
