Topological version of section theorems with applications

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

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.     

Generalized variational inequalities and generalized quasi-variational inequalities

Under much weaker hypotheses and in a more general setting some existence theorems of solutions to generalized variational inequalities,generalized quasi-varia-tional inequalities and minimax inequalities are established.The results presented in this paper generalize the corresponding results of[3—13]to the noncompact case,thus improving these results.     

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.     

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...     

Intersection theorems concerning noncompact sets with H-convex sections and their applications

In this paper,we prove some intersection theorems concerning noncompact sets withH-convex sections which generalize the corresponding results of Ma.Fan,Tarafdar,Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting.An application to von Neumann type minimax theorems is given.     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)

By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.     

Topologically finite intersection property and minimax theorems

ＴＯＰＯＬＯＧＩＣＡＬＬＹＦＩＮＩＴＥＩＮＴＥＲＳＥＣＴＩＯＮＰＲＯＰＥＲＴＹＡＮＤＭＩＮＩＭＡＸＴＨＥＯＲＥＭＳＺｈａｎｇＳｈｉ－ｓｈｅｎｇ（张石生）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄ...     

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.     

Existence of solutions for generalized quasi-variational-like inequalities

ProjectsupportedbytheNationalNaturalScienceFoundationofChinaI.Introduction'LetEandFbetopologicalvectorspaceswithsamescalarfielddi(eithertherealfieldorthecomplexfield)andXbeanonempt}'subsetofE.Let<',.):FxE-dibeabilinearfunctional,j:X-Fbeasingle-valuedmappi…     

NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 991 ,Ｔａｒａｆｄａｒ[1]ｆｉｒｓｔｅｓｔａｂｌｉｓｈｅｄｔｈｅｆｏｌｌｏｗｉｎｇｃｏｌｌｅｃｔｉｖｅｌｙｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｏｎｔｈｅｐｒｏｄｕｃｔｓｐａｃｅｏｆｎｏｎｅｍｐｔｙｃｏｍｐａｃｔｃｏｎｖｅｘｓｕｂｓｅｔｓｏｆｔｏｐｏｌｏｇｉｃａｌｖｅｃｔｏｒｓｐａｃｅｓａｎｄｇａｖｅｉｔｓａｐｐｌｉｃａｔｉｏｎｓｔｏｔｈｅｅｘｉｓｔｅｎｃｅｏｆｅｑｕｉｌｉｂｒｉｕｍｐｏｉｎｔｓｆｏｒａｂｓｔｒａｃｔｅｃｏｎｏｍｉｅｓ.Ｔｈｅｏｒｅｍ 1　Ｌｅｔ Ｘｉ ｉ∈Ｉ…     

Algorithm of solutions for mixed-nonlinear variational-like inequalities in reflexive banach space

I.IntroductionLetDbeanonemptyconvexsubsetofaBanachspaceB,BbethetopologicaldualspaceofBand(u,v)bethepairingbetweenneBandr6B.LetT,A:D~B'and9:DxD-Bbethreemappingsandf:D~(-ac, ac1beareal-valuedfunction.Inthispaper,weshallinvestigatethemixednonlinearvariationalinequalityproblemMNna(T,A,9,f,D):FinduEDsuchthatSpecialCases.(l)f-0,thentheproblem(l.l)isequivalenttofindingueDsuchthatTheproblem(l.2)isthestronglynonlinearvariational-likeinequalityproblemstudiedbyNoorllJwhicharisesnaturallyincon…     

GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｒｅｅ＿ｄｉｍｅｎｓｉｏｎａｌｐｈｏｔｏｅｌａｓｔｉｃｉｔｙ ,ｐｈｏｔｏｐｌａｓｔｉｃｉｔｙ ,ｓｉｍｕｌａｔｉｎｇｅｘｐｅｒｉｍｅｎｔｓｏｆｂｕｉｌｄｉｎｇｓｔｒｕｃｔｕｒｅｓａｎｄｐｈｙｓｉｃａｌｓｉｍｕｌａｔｉｏｎｓｏｆｍｅｔａｌｆｏｒｍｉｎｇｐｒｏｃｅｓｓｅｓ,ｔｈｅｒｅｉｓｅａｃｈａｎｄａｌｌａｎｉｄｅｎｔｉｃａｌｐｒｏｂｌｅｍｓｆｏｒｓｔｕｄｙ ,ｔｈａｔｉｓ,ｇｒｅａｔｅｒｒｏｒｓａｒｅｕｓｕａｌｌｙｃａｕｓｅｄｂｙｔｈｅｓｕｐｐｏｓｉｔｉｏｎｔｈａｔｔｈ…     

Caristi type hybrid fixed point theorems in menger probabilistic metric space

I.IntroductionandPreliminariesInl976,CaristiprovedtheCaristi'sfixedpointtheoreminIll.Becausethistheoremdoesnotrequirethecontinuityofthemapping.ittindsapplicationsinmanyfields.Inl99l,S.S.Changetal.l'l,broughtforwardCaristi'sfixedpointtheoremandEkeland'svar…     

The extension theorems of cone linear operators

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｅｘｔｅｎｓｉｏｎｔｈｅｏｒｅｍｏｆｔｈｅｌｉｎｅａｒｆｕｎｃｔｉｏｎａｌｉｓｏｎｅｏｆｔｈｅｂａｓｉｃｔｈｅｏｒｅｍｓｉｎｆｕｎｃｔｉｏｎａｌａｎａｌｙｓｉｓ.Ｉｔｈａｓｂｅｅｎｅｘｔｅｎｄｅｄｔｏｍａｎｙｆｏｒｍｓ,ａｎｄ ,ｏｆｃｏｕｒｓｅ,ｈａｓｆｏｕｎｄｍａｎｙｉｍｐｏｒｔａｎｔａｐｐｌｉｃａｔｉｏｎｉｎｓｕｃｈｆｉｅｌｄｓａｓｎｏｎｓｍｏｏｔｈａｎａｌｙｓｉｓ,ｏｐｔｉｍｉｚａｔｉｏｎａｎｄｖａｒｉａｔｉｏｎａｌｐｒｏｂｌｅ…     

Generalized reciprocal theorems and their applications

Generalized reciprocal theorems of non-coupled and coupled systems, which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti's reciprocal theorem. When the consitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti's. Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity. Foundation item: the National Major Laboratory of Plastic Forming Simulation and Die Arrangement Technology (991-6) Biography: FU Bao-lian (1934-)     

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.     

Probabilistic norm of operators and resonance theorems

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｓｔ,ａｓｔｈｅｄｅｆｉｎｉｔｉｏｎｓａｂｏｕｔｓｏｍｅｃｏｎｃｅｐｔｓｉｎｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅ（ｂｒｉｅｆｌｙ,ＰＮｓｐａｃｅ）ｃｏｐｉｅｄｔｈｅｃｏｒｅｓｐｏｎｄｉｎｇ...     

Some generalizations of generalized bi-quasivariational inequalities

The purpose of this paper is to introduce and study the existenee problems of solutions for a class of new bi-quasi-variational inequalities. The resuhs presented in this paper unify, sharpen and extend many recent results.     

Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces

In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.