Constrained multiobjective games in locally convex<Emphasis Type="Italic">H</Emphasis>-spaces

A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied. By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem, several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces. These theorems improve, unify and generalize the corresponding results of the multiobjective games in recent literatures. Contributed by Ding Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Ding Xie-ping (1938-)     

Quasi-Equilibrium Problems and Constrained Multiobjective Games in Generalized Convex Space

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2 ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ .ＬｅｔＴ :Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,Ａ :Ｘ→ 2 Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇ ,ψ :Ｘ×Ｙ×Ｘ→Ｒ∪ ±∞ ａｎｄｆ:Ｘ×Ｙ→Ｒ∪ ±∞ ｂｅｔｗｏｆｕｎｃｔｉｏｎｓ.Ｔｈｅｇｅｎｅｒａｌｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＧＱＥＰ (Ｔ ,Ａ ,ψ)ｉｓｔｏｆｉｎｄ ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ( ^ｘ) ,ψ( ^ｘ ,Ｔ^ｘ ,ｙ)≤ 0…     

Generalized constrained multiobjective games in locally <Emphasis Type="Italic">FC</Emphasis>-uniform spaces

A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.     

Noncompact infinite optimization and equilibria of constrained games in generalized convex spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＩｂｅａｎｙ (ｆｉｎｉｔｅｏｒｉｎｆｉｎｉｔｅ)ｉｎｄｅｘｓｅｔａｎｄｆｏｒｅａｃｈｉ∈Ｉ,Ｘｉｂｅａｔｏｐｏｌｏｇｉｃａｌｓｐａｃｅ.ＷｅｕｓｅｔｈｅｎｏｔａｔｉｏｎＸ =∏ｉ∈ＩＸｉ　ａｎｄ　Ｘｉ=∏ｊ∈Ｉ,ｊ≠ｉＸｊ.Ｆｏｒｅａｃｈｘ∈Ｘ ,ｘｉｄｅｎｏｔｅｓｉｔｓｉｔｈｃｏｏｒｄｉｎａｔｅａｎｄｘｉｔｈｅｐｒｏｊｅｃｔｉｏｎｏｆｘｏｎＸｉ.Ｗｒｉｔｅｘ=(ｘｉ,ｘｉ) .Ｆｏｒｅａｃｈｉ∈Ｉ,ｌｅｔＦｉ:Ｘｉ → 2 Ｘｉｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇａｎｄｆｉ:Ｘ →Ｒ …     

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES

IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ .　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 1 )　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 2 )　　…     

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.     

CONTINUOUS SELECTION THEOREMS FOR FAN-BROWDER MAPPINGS IN TOPOLOGICAL SPACES AND THEIR APPLICATIONS

The concept of Fan-Browder mappings was first introduced in topological spaces without any convex structure. Then a new continuous selection theorem was obtained for the Fan-Browder mapping with range in a topological space without any convex structure and noncompact domain. As applications, some fixed point theorems, coincidence theorems and a nonempty intersection theorem were given. Both the new concepts and results unify and extend many known results in recent literature.     

Quasi-equilibrium problems in noncompact generalized convex spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸａｎｄＹｂｅｎｏｎｅｍｐｔｙｓｅｔｓａｎｄ2ＸｂｅｔｈｅｆａｍｉｌｙｏｆａｌｌｓｕｂｓｅｔｓｏｆＸ.ＬｅｔＴ:Ｘ→Ｙｂｅａｓｉｎｇｌｅ＿ｖａｌｕｅｄｍａｐｐｉｎｇ,Ａ:Ｘ→2Ｘｂｅａｓｅｔ＿ｖａｌｕｅｄｍａｐｐｉｎｇａｎｄｆ:Ｘ×Ｙ→Ｒ∪±∞ｂｅａｆｕｎｃｔｉｏｎ.Ｔｈｅｑｕａｓｉ＿ｅｑｕｉｌｉｂｒｉｕｍｐｒｏｂｌｅｍＱＥＰ(Ｔ,Ａ,ｆ)ｉｓｔｏｆｉｎｄ^ｘ∈Ｘｓｕｃｈｔｈａｔ^ｘ∈Ａ(^ｘ),ｆ(^ｘ,Ｔ^ｘ)≤ｆ(ｙ,Ｔ^ｘ),　　ｙ∈Ａ(^ｘ).(1)ＴｈｅＱＥＰ(Ｔ,Ａ,ｆ)ｗａｓｉｎｔｒｏｄ…     

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

IntroductionItiswell_knownthattheexistenceofmaximalelementsforset_valuedmappingsintopological(vector)spacesanditsimportantapplicationstomathematicaleconomieshavebeenstudiedextensivelybymanyauthorsinbothmathematicsandeconomics.Forexistenceresultsofmaximalelementsofvariousclassesofset_valuedmappingsandtheirapplicationstomathematicaleconomiesandotherbranchesofmathematics,thereadermayconsultRefs.[1～ 2 7]andthereferencestherein .LetXbeatopologicalspaceandY =∏i∈IYibeaproductofnonemptyconvexsetY…     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

IntroductionThispaperisacontinuumoftheprecedingpaperofauthor[1] .Fortheconceptsandnotationsofgeneralizedconvex (orG_convex)space ,CG_convexspace,theclassB(Y ,X)ofbetteradmissiblemappings ,GB_mappings,GB_majorizedmappingsandtherelatednotions,thereadermayconsultRef.[1].Themainaimofthispaperistogivesomeapplicationsoftheexistencetheoremsofmaximalelementsobtainedbyauthor[1] .ByapplyingourresultsinRef.[1],wegivesomecomponentversionofcoincidencetheoremandFan_Browdertypefixedpointtheorems .Somee…     

Covering properties on H-spaces and applications

Several theorems on closed(resp.open)covering properties of H-spaces areobtained which improve and generalize the corresponding results of Sperner,Klee,Alexandroff-Pasynkoff,Berge,Ghouila-Houri,Danzer-Gr(?)nbaum-Klee,Ky Fan,Shih-Tan,Horvath and Lassonde.As application an almost fixed point theorem for lowersemi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed pointtheorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.     

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

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

A new equilibrium existence theorem of generalized game

ＡＮＥＷＥＱＵＩＬＩＢＲＩＵＭＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＯＦＧＥＮＥＲＡＬＩＺＥＤＧＡＭＥＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＡＮＥＷＥＱＵＩＬＩＢＲＩＵＭＥＸＩＳＴＥＮＣＥＴＨＥ...     

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

A new notion of finite continuous topological space (in short, FC-space) with out convexity structure was introduced. A new continuous selection theorem was established in FC-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper.     

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

A new notion of finite continuous topological space (in short, FC-space)with out convexity structure was introduced. A new continuous selection theorem was established in FC-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper.     

MAXIMAL ELEMENTS FOR G-B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)

By applying existence theorems of maximal elements for a family of G_B-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. Contributed by Duping Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn)     

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.     

Maximal Elements and Equilibrium of Abstract Economy

ＩｎｔｒｏｄｕｃｔｉｏｎＧｅｏｒｇｅＸｉａｎＺｈｉＹｕａｎａｎｄＥ .Ｔａｒａｆｄａｒｉｎ [1 ]ｐｒｏｖｅｄｔｈｅｆｏｌｌｏｗｉｎｇｅｘｉｓｔｅｎｃｅｔｈｅｏｒｅｍｏｆｍａｘｉｍａｌｅｌｅｍｅｎｔｓｆｏｒａｎｅｗｔｙｐｅｏｆｐｒｅｆｅｒｅｎｃｅｃｏｒｒｅｓｐｏｎｄｅｎｃｅｓｗｈｉｃｈａｒｅμ＿ｍａｊｏｒｉｚｅｄ .ＴｈｅｏｒｅｍＡ　ＬｅｔＸｂｅａｎｏｎｅｍｐｔｙｃｏｎｖｅｘｓｕｂｓｅｔｏｆａＨａｕｓｄｏｒｆｆｌｏｃａｌｌｙｃｏｎｖｅｘｔｏｐｏｌｏｇｉｃａｌｖｅｃｔｏｒｓｐａｃｅａｎｄｌｅｔＤｂｅａｎ…     

Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.