The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on H-spaces.As a way of application,we use these results to study the existence problems of solutions for minim...The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on H-spaces.As a way of application,we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities.The results presented in this paper improve and extend the corresponding results in[1,3,5,6,8,9,12,14,15,17]展开更多
In this paper, the author gives a new section theorem in L-convex spaces. And as its applications, the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.
In this paper some new types of KKM theorem and section theorems are given.As applications, the existence problems of solutions for three kinds of variationalinequalities and fixed point problem for set-valued mapping...In this paper some new types of KKM theorem and section theorems are given.As applications, the existence problems of solutions for three kinds of variationalinequalities and fixed point problem for set-valued mapping have been siudied by usingthose results. The results presented in this paper improve and extend the main resultsin [1 - 19].展开更多
If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding ...If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn（K）≤μn（L）. This extends a generalized Funk＇s section theorem for volumes to that for measures.展开更多
The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bod...The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.展开更多
In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.
In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities...In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on H-spaces.As a way of application,we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities.The results presented in this paper improve and extend the corresponding results in[1,3,5,6,8,9,12,14,15,17]
基金the Scientific Research Common Program of Beijing Municipal Commission of Education(KM200610005014)
文摘In this paper, the author gives a new section theorem in L-convex spaces. And as its applications, the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.
文摘In this paper some new types of KKM theorem and section theorems are given.As applications, the existence problems of solutions for three kinds of variationalinequalities and fixed point problem for set-valued mapping have been siudied by usingthose results. The results presented in this paper improve and extend the main resultsin [1 - 19].
基金Supported by the National Natural Science Foundation of China(10801140)Chongqing Research Program of Basic Research and Frontier Technology(2013-JCYJ-A00005)the Foundation of Chongqing Normal University(13XLZ05)
文摘If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn（K）≤μn（L）. This extends a generalized Funk＇s section theorem for volumes to that for measures.
文摘The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.
文摘In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.
文摘In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.
