FC_空间中的参数型KKM定理及其应用

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.     

KKM technique and its applications

In this paper,the Knaster-Karatowski-Mazurkiewicz technique(KKM technique,in short)is presented.By using this technique a new alternative theorem and a new coincidence theorem are established.The results obtained in this paper unify and generalize the corresponding results in the recent works.     

Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.     

A new streamline diffusion finite element method for the generalized Oseen problem

This paper aims to present a new streamline diffusion method with low order rectangular Bernardi-Raugel elements to solve the generalized Oseen equations. With the help of the Bramble-Hilbert lemma, the optimal errors of the velocity and pressure are estimated, which are independent of the considered parameter ε. With an interpolation postprocessing approach, the superconvergent error of the pressure is obtained. Finally,a numerical experiment is carried out to confirm the theoretical results.     

G-凸空间的择一原理和极大极小不等式

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.     

Topological version of section theorems with applications

ＴＯＰＯＬＯＧＩＣＡＬＶＥＲＳＩＯＮＯＦＳＥＣＴＩＯＮＴＨＥＯＲＥＭＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉ－ｓｈｅｎｇ（张石生）（ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＷｕＸｉａｎ（吴鲜）（ＺｈａｏｔｏｎｇＴｅａｃｈｅｒ’ｓ...     

MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE

I.IntroductionFanKyinequalityisaveryusefultoolinnoolinearanalysiswhichasserts:LetXbeanonemptycompactconvexsetinatopologicallinearspaceandWbeareal-valuedfunctiondefinedonXxX.Assumethat(i)9(x,y)islowersemicontinuousinac;(n)9(x,y)isquasiconcaveiny.ThenthereisboaXsuchthatsHPg(xo'Y)$sZPp(x,x).SinceFanKyprovedtheinequalityin1972,variousg...,.li..tlon,havebeen;v..byseveralauthors(see[l-3]andreferencestherein).Thepreviousgeneralizationsallremainedtheconditions(i)-'9(x,y)beinglowersemicontinuous…     

Generalized minimax inequalities and fixed point theorems

Recently,many authors have generalized the famous Ky Fan’s minimaxinequality.In this paper,we put forward T-diagonal convexity(concavity)conditions anddevelop the main results in this respect.Next.we discuss some fixed point problems,andgeneralize the Fan-Glicksberg’s fixed point theorem.     

On the existence and uniqueness of solutions for a class of variational inequalities with applications to the signorini problem in mechanics

In this paper,we introduce a new unified and general class of variational inequalities,and show some existence and uniqueness results of solutions for this kind of variationalinequalities.As an application,we utilize the results presented in this paper to study theSignorini problem in mechanics.     

NEW VERSION OF KKMTHEOREM IN PROBABILISTIC METRIC SPACES WITH APPLICATIONS

ＮＥＷＶＥＲＳＩＯＮＯＦＫＫＭＴＨＥＯＲＥＭＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）ＹｅｏｌＪｅＣｈｏ（赵烈济）ＷｕＸｉａｎｇ（吴鲜）（ＲｅｃｅｉｖｅｄＭａｙ７，１９９...     

Section theorems,coincidence theorems and intersection theorems on H-spaces with applications

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]     

A generalization of Browder's fixed point theorem with applications

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＩｎ１９６８,Ｂｒｏｗｄｅｒ［１］ｐｒｏｖｅｄｔｈｅｆｏｌｌｏｗｉｎｇｔｈｅｏｒｅｍ．Ｔｈｅｏｒｅｍ１１（Ｂｒｏｗｄｅｒ［１］）　ＬｅｔＥｂｅａＨａｕｓｄｏｒｆｆｔｏｐｏｌｏｇｉｃａｌｌｉｎｅａｒｓｐａｃｅ,ＸａｃｏｍｐａｃｔｃｏｎｖｅｘｓｕｂｓｅｔｏｆＥａｎｄＦ：Ｘ→２Ｘａｍａｐｐｉｎｇｓａｔｉｓｆｙｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉｔｉｏｎｓ：ⅰ）Ｆｏｒａｎｙｘ∈Ｘ,Ｆ（ｘ）ｉｓｎｏｎｅｍｐｔｙａｎｄｃｏｎｖｅｘ;ⅱ）Ｆｏｒａ…     

Fixed point index of uniform limit of set-Valued strict set-contractive mappings and its applications

In this paper,the class of uniform limit mappings of set-valued,strick set-contractivemappings is discussed.Furthermore,the fixed point index theory for the uniform limitmappings is established.Using the fixed point index theory,some positive fixed pointtheorems are proved.Our theorems generalize some results in[1,4,5,7].     

A parametric type of KKM theorem in <Emphasis Type="Italic">FC</Emphasis>-spaces with applications

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.     

A general topological version of minimax theorem

ＡＧＥＮＥＲＡＬＴＯＰＯＬＯＧＩＣＡＬＶＥＲＳＩＯＮＯＦＭＩＮＩＭＡＸＴＨＥＯＲＥＭＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ６１００６４,Ｐ．Ｒ．Ｃｈｉｎ...     

Effect of magnetic field on poroelastic bone model for internal remodeling

This paper studies the effects of the magnetic field and the porosity on a poroelastic bone model for internal remodeling. The solution of the internal bone remodeling process induced by a magnetic field is presented. The bone is treated as a poroelastic material by Biot’s formulation. Based on the theory of small strain adaptive elasticity, a theoretical approach for the internal remodeling is proposed. The components of the stresses, the displacements, and the rate of internal remodeling are obtained in analytical forms, and the numerical results are represented graphically. The results indicate that the effects of the magnetic field and the porosity on the rate of internal remodeling in bone are very pronounced.     

TRANSFER OPEN OR CLOSED SETVALUED MAPPING AND GENERALIZ－ATION OF H－KKM THEOREM WITH APPLICATIONS

ＴＲＡＮＳＦＥＲＯＰＥＮＯＲＣＬＯＳＥＤＳＥＴＶＡＬＵＥＤＭＡＰＰＩＮＧＡＮＤＧＥＮＥＲＡＬＩＺ－ＡＴＩＯＮＯＦＨ－ＫＫＭＴＨＥＯＲＥＭＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＬｉＢｉｎｇ－ｙｏｕ（李秉友）;ＳｕＪｉａ－ｂａｏ（苏家宝）（Ｄｅｐａｒｔｍｅｎｔ...     

New collectively fixed point theorems and applications inG-convex spaces

By applying the technique of continuous partition of unity and Tychonoff’s fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.     

Some results of variational inclusion problems and fixed point problems with applications

This paper introduces a general iterative algorithm to approximate a common element in the solution set of quasi-variational inclusion problems and the common fixed point set of an infinite family of nonexpansive mappings. It is proven that the iterative sequences generated in the proposed iterative algorithm converge strongly to some common element in the framework of the real Hilbert spaces.     

关于变分不等式问题近似解的数值证明

基于文献[1]给出了一种数值证明变分不等式解的存在性方法。通过Hilbert空间中的Riesz表示定理,首先将变分不等式问题的迭代过程转化为一种不动点形式,再利用Schauder不动点定理构造了一个高效率的数值证明过程,即通过数值计算产生一个包含近似解的有界闭凸子集。非线性Helmholtz方程的算例说明这一方法的可行性和高效性。