Some new fixed point theorems in probabilistic metric spaces

ＳＯＭＥＮＥＷＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳｚｈｕＣｈｕａｎ－ｘｉ（朱传喜）（ＭａｔｈｅｍａｔｉｅｓＤｉｖｉｓｉｏｎ,Ｎａｎｃｈａｎｇ．Ｕｎｉｖｅｒｓｉｔｙ,Ｎａｎｃｈａｎｇ）（Ｒｅｃｅｉｖ...     

EKELAND’S VARIATIONAL PRINCIPLE AND CARISTI’S COINCIDENCE THEOREM FOR SET-VALUED MAPPINGS IN PROBABILISTIC METRIC SPACES

By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.     

Probabilistic contractor couple and solutions for a system of nonlinear equations in non-archimedean menger probabilistic normed spaces

The Purpose of this paper is to introduce the concept of probabilistic contractor couple in non-Archimedean probabilistic normed spaces and to study the existence and uniqueness of solutions for a system of nonlinear operator equations with probabilistic contractor couples in non-Archimedean probabilistic normed spaces.The results presented in this paper improve and extend the corresponding results in[1-5].     

On probabilistic norm of a linear operators and space of operators

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］,ＸｉａｏｉｎｔｒｏｄｕｃｅｄｔｈｅｎｏｔｉｏｎｏｆｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｏｆａｌｉｎｅａｒｏｐｅｒａｔｏｒｏｎＭｅｎｇｅｒｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｅｄｓｐａｃｅ（ｂｒｉｅｆｙ,ＭｅｎｇｅｒＰＮ＿ｓｐａｃｅ）．Ａｎｄｂｙｕｓｉｎｇｔｈｅｎｏｔｉｏｎ,ｕｎｄｅｒｔｈｅｃｏｎｄｉｔｉｏｎｏｆｔ＿ｎｏｒｍΔｓａｔｉｓｆｙｉｎｇΔ（ｔ,ｔ）≥ｔ（ｔ∈（０,１］）,ｈｅｇａｖｅａｄｅｓｃｒｉｐｔｉｏｎｏｆｂｏｕｎｄｅｄｎｅｓｓｏｆｌｉｎｅａｒｏｐｅ…     

Coincidence point theorems in probabilistic metric spaces with a convex structures

ＣＯＩＮＣＩＤＥＮＣＥＰＯＩＮＴＴＨＥＯＲＥＭＳｉＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳＷＩＴＨＡＣＯＮＶＥＸＳＴＲＵＣＴＵＲＥＳＷｅｅＴａｅＰａｒｋ（朴渭汰）ＫｅｕｎＳａｅｎｇＰａｒｋ（朴根生）ＹｅｏｌＪｅＣｈｏ（赵烈济）（Ｄｅｐａｒ...     

The theory and applications of generalized H-space

This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces.In this paper,the uniformity and properties far generalized H-space are considered.The conditions of metrization and the form of metric functions for generalized H-spaces,H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented.The results of this paper generalize and unify some recent results of[1-2,8,10].     

Random fixed point theorems for commuting random operators in probabilistic functional analysis

Random fixed point theorems are of fundamental importance in probabilistic functional analysis. In complete separable metric space random fixed point theorems have been discussed by Bharucha-Reidf1/27, Hans[3], Itohf4,5J and the author’s papers[15-20].In this paper we obtain a random fixed point theorem for commuting random operators in probabilistic functional analysis. Our results generalize some important results also extend and unify some results in Jungck[6,7,8]t Das and Naiki[9] as well as Bhoades[10] adn ciric[11].     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

ＦＩＸＥＤ　ＰＯＩＮＴ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＦＵＺＺＹ　ＭＡＰＰＩＮＧＳ　ＩＮ　ＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＥＴＲＩＣ　ＳＰＡＣＥＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）；ＺｈａｎｇＹｉｎｇ（张颖）；ＹｕａｎＪｉａｗｅｉ（袁家玮）（Ｒｅｃｅｉｖ...     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅰ)

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.     

Nonlinear semigroups and differential inclusions in probabilistic normed spaces

I.IntroductionTheconceptofaccretivemappingsisoffundamentalimportanceinthetheoryofsetvaluednonlinearoperators,differentialequationsandpartialdifferentialequationsinBanachspaces,whichwasintroducedindependentlybyF.E.Browdert31andT.Katolll].Ontheotherhand,manyauthorshavedoneconsiderableworkonsemigroupsofnonlinearcontractions,differentialequationsandevolutionequationsinBanachspacesandHilbertspaceal"='4'?.8.l:,13j.Recently,theauthorsintroducedtheconceptofaccretivemappingst"andsomeelementaryprope…     

The embedded theorem for family of quasi metric spaces in Menger space and its application

In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition. The proving technique herein seems to be new even for mappings in Menger spaces.     

FIXED POINT THEOREMS FOR MAPPINGS SATISFYING IMPLICIT RELATION ON TWO COMPLETE AND COMPACT METRIC SPACES

First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.     

On the isometric isomorphism of probabilistic metric spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅａｒｅｔｗｏｋｉｎｄｓｏｆｉｓｏｍｅｔｒｉｃｉｓｏｍｏｒｐｈｉｓｍｉｎｐｒｏｂａｂｉｌｉｓｔｉｃｍｅｔｒｉｃｓｐａｃｅｔｈｅｏｒｙ (ｓｅｅ[1 -9] ) .ＴｈｅｆｉｒｓｔｉｓｔｈａｔａＰＭｓｐａｃｅ (Ｅ ,Ｆ)ｉｓｉｓｏｍｅｔｒｉｃａｌｌｙｉｓｏｍｏｒｐｈｉｃｔｏａｎｏｔｈｅｒＰＭｓｐａｃｅ(Ｅ′,Ｆ′) ,ａｎｄｔｈｅｓｅｃｏｎｄｉｓｔｈａｔａＰＭｓｐａｃｅｓ(Ｅ ,Ｆ)ｉｓｉｓｏｍｅｔｒｉｃａｌｌｙｉｓｏｍｏｒｐｈｉｃｔｏａｇｅｎｅｒａｔｉｎｇｓｐａｃｅｏｆｑｕａｓｉ＿ｍｅｔ…     

Lie symmetries of geodesic equations and projective collineations

We prove a theorem which relates the Lie symmetries of the geodesic equations in a Riemannian space with the collineations of the metric. We apply the results to Einstein spaces and spaces of constant curvature. Finally with examples we show the use of the results.     

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without con-vexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the sys-tems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vec-tor quasi-optimization problems.     

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

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.     

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.     

Fixed points of a pair of asymptotically regular mappings

I.IntroductionTheconceptofasymptoticregularitywasintroducedbyBrowderandPetryshynl'].LetEbearealBanachspacewithnorn11l'l'AmappingT:E-Eissaidtobeasymptotical1yregulariflimijT" 'x~T'x:l=ofora1lxinE,whereTffxdenotesthenthiteratio11of--ooT.ltiswell-knownthatif…     

Existence and stability of common fixed points for systems of mappings

In this paper,we establish some common fixed point theorems and stability theorems of the sets of common fixed points for the systems of set-valued and single-valued nonlinear contractive type mappings in a finite Cartesian product of metric spaces.     

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.