In my former paper ＂A pre-order principle and set-valued Ekeland variational principle＂ （see [J. Math. Anal. Applo, 419, 904 937 （2014）]）, we established a general pre-order principle. From the pre-order princip...In my former paper ＂A pre-order principle and set-valued Ekeland variational principle＂ （see [J. Math. Anal. Applo, 419, 904 937 （2014）]）, we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles （denoted by EVPs） in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy＇s EVP in [On generalized Ekeland＇s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381-396 （2011）], where the perturbation contains a weak T-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy＇s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11471236 and 11561049)
文摘In my former paper ＂A pre-order principle and set-valued Ekeland variational principle＂ （see [J. Math. Anal. Applo, 419, 904 937 （2014）]）, we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles （denoted by EVPs） in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy＇s EVP in [On generalized Ekeland＇s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381-396 （2011）], where the perturbation contains a weak T-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy＇s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.
