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1.
王广民 《应用数学和力学(英文版)》2007,28(12):1561-1568
First, the notions of the measure of noncompactness and condensing set-valued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings
involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings
are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems
will be given in a follow-up paper.
Project supported by the Natural Science Foundation of Sichuan Education Department of China (Nos. 2003A081 and SZD0406) 相似文献
2.
Servet Kutukcu Adnan Tuna Atakan T. Yakut 《应用数学和力学(英文版)》2007,28(6):799-809
Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces. 相似文献
3.
方锦暄 《应用数学和力学(英文版)》1999,20(10):1160-1166
IntroductionIn[1],XiaointroducedthenotionofprobabilisticnormofalinearoperatoronMengerprobabilisticnormedspace(briefy,MengerPN_space).Andbyusingthenotion,undertheconditionoft_normΔsatisfyingΔ(t,t)≥t(t∈(0,1]),hegaveadescriptionofboundednessoflinearope… 相似文献
4.
丁协平 《应用数学和力学(英文版)》2007,28(12):1569-1579
This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems
involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized
vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces.
Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406) 相似文献
5.
The Leray-Schauder topological degree theory is established in the probabilistic linear normed spaces. Based on this theory, some fixed point theorems for mappings in the probabilistic linear normed spaces are shown.The projects supported by National Natural Science Foundation of China. 相似文献
6.
曾六川 《应用数学和力学(英文版)》2003,24(12):1421-1430
IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E →2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉=‖x‖·‖f‖,‖f‖=‖x‖, x∈E . Definition 1 LetT :D →Dbeamapping .1 )Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞)withlimn→∞kn =1suchthat ‖Tnx-Tny‖≤kn‖x-y‖forall x ,y∈D ,n≥0 ;(1 ) 2 )Tissaidtobeofasymptoticallynonexpansivetype[2 ],if lims… 相似文献
7.
DING Xie-ping 《应用数学和力学(英文版)》2007,28(12)
First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications,some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper. 相似文献
8.
Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces 总被引:1,自引:0,他引:1
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. 相似文献
9.
Some new fixed point theorems in probabilistic metric spaces 总被引:21,自引:0,他引:21
朱传喜 《应用数学和力学(英文版)》1995,16(2):179-185
SOMENEWFIXEDPOINTTHEOREMSINPROBABILISTICMETRICSPACESzhuChuan-xi(朱传喜)(MathematiesDivision,Nanchang.University,Nanchang)(Receiv... 相似文献
10.
I.IntroductionTheconceptofaccretivemappingsisoffundamentalimportanceinthetheoryofsetvaluednonlinearoperators,differentialequationsandpartialdifferentialequationsinBanachspaces,whichwasintroducedindependentlybyF.E.Browdert31andT.Katolll].Ontheotherhand,manyauthorshavedoneconsiderableworkonsemigroupsofnonlinearcontractions,differentialequationsandevolutionequationsinBanachspacesandHilbertspaceal"='4'?.8.l:,13j.Recently,theauthorsintroducedtheconceptofaccretivemappingst"andsomeelementaryprope… 相似文献
11.
DING Xie-ping College of Mathematics Software Science Sichuan Normal University Chengdu P.R.China 《应用数学和力学(英文版)》2007,(12)
First,the notions of the measure of noncompactnees and condensing set- valued mappings are introduced in locally FC-uniform spaces without convexity struc- ture.A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces.As applications, some new equilibrium existence theorems of generalized game involving condensing map- pings are established in locally FC-uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper. 相似文献
12.
丁协平 《应用数学和力学(英文版)》2007,(12)
This paper is a continuum of the preceding paper of author.Some new sys- tems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces.By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper,some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC- uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces. 相似文献
13.
DING Xie-ping 《应用数学和力学(英文版)》2007,28(12)
This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. 相似文献
14.
曾六川 《应用数学和力学(英文版)》2003,24(3):344-354
IntroductionLetKbeanonemptysubsetofaBanachspaceX .ThenamappingT :K→KissaidtobeaLipschitzianmappingif,foreachintegern≥ 1 ,thereexistsaconstantkn >0suchthat‖Tnx-Tny‖ ≤kn‖x-y‖ forallx ,y∈K .ALipschitzianmappingTissaidtobeuniformlyk_Lipschitzianifkn =kforalln ≥ 1 ;no… 相似文献
15.
BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅰ) 总被引:1,自引:1,他引:1
Zhang Shi-sheng 《应用数学和力学(英文版)》1988,9(2):123-133
This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this
paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of
metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given and the characterizations
of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to
study the linear operator theory and fixed point theory on PM-spaces.
Projects supported by the Science Fund of the Chinese Academy of Sciences. 相似文献
16.
丁协平 《应用数学和力学(英文版)》1987,8(3):211-218
The author defines a concept of fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces. Using this concept, the author establishes several nonzero fixed point theorems of set-valued -condensing mappings. These theorems extend some known results in [1,2,7,8,9].Projects Supported by the Science Fund of the Chinese Academy of Sciences 相似文献
17.
The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for
generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values
were established in H-metric spaces. These theorems generalized recent results of Khamsi and Yuan. As applications, some Ky
Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers,
fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of know results
in recent literature.
Paper from DING Xie-ping, Member of Editoral Committee, AMM
Foundation item: the National Natural Science Foundation of China (19871059)
Biography: DING Xie-ping (1938-), Professor 相似文献
18.
In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature. 相似文献
19.
IntroductionIn 1 991 ,Tarafdar[1]firstestablishedthefollowingcollectivelyfixedpointtheoremontheproductspaceofnonemptycompactconvexsubsetsoftopologicalvectorspacesandgaveitsapplicationstotheexistenceofequilibriumpointsforabstracteconomies.Theorem 1 Let Xi i∈I… 相似文献
20.
IntroductionIn 1 996,Khamsi[1]establishedthehyperconvexversionofthefamousFan_KKMprincipleinhyperconvexspace .Yuan[2 ,3]obtainsomecharacterizationofKKMprincipleinhyperconvexspaces,andasapplicationsoftheirresults,somefixedpointtheoremsandmatchingtheoremsforopena… 相似文献