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…     

PANSYMMETRY AND FIXED PANSYSTEMS THEOREMS OF A CLASS OF PANSYSTEMS RELATIONS

In this paper. some results of pansymmetry and fixed pansystems theorems areextended to the case of a class of binary relations under the framework of pansystemsmethodology It is concretely discussed when a class of binary relations has a common fixedsubset on a finite universal set. Several simple but comprehensive decisive theorems areobtained which can be determined if a class of binary relations has a common fixed subset.Asaresult the main decisive theorem-Markov-Kakutani Theorem-is extended whichis in traditionally fixed point theory and can be determined if a class of mappings has acommon fixed point.     

Random common fixed point theorems of set-valued mappings

In this paper, we prove several random common fixed point theorems to general setvalued contractive mappings. These theorems improve and generalize the corresponding results in [1–18].     

Coincidence point theorems in probabilistic metric spaces with a convex structures

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

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

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].     

Pansystems research on a type of fixed subsets

The present paper continues the pansystems research on fixed studies. Under the pansystems framework it gives the existence critertion of I-type fixed and the theorems about the relations between the classes of reflexive and equation one and fixed subsets: introdaces the concept of fixpoints of binary relations extstence theorems about fixpoints for a kind of panweighted netwest.     

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...     

The description of the characteristics of the structure and the quantity in fixed pansystems theorems

Pansymmetry is the abstract of symetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the Work in concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.     

Some new fixed point theorems in probabilistic metric spaces

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

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

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

Some new results about fixed pansystems theorems

In this paper the fixed pansystems theorems concerning the composition-complement-operators are discussed.Some existence conditions of panchaos and strange panattractor are given.And using the results,some fixed point theorems for many-valued mappings are also proved,which complement and develop the results obtained by Kakutani.     

On the existence of common fixed points for a pair of lipschitzian mappings in banach spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＫｂｅａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆａＢａｎａｃｈｓｐａｃｅＸ .ＴｈｅｎａｍａｐｐｉｎｇＴ :Ｋ→ＫｉｓｓａｉｄｔｏｂｅａＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇｉｆ,ｆｏｒｅａｃｈｉｎｔｅｇｅｒｎ≥ 1 ,ｔｈｅｒｅｅｘｉｓｔｓａｃｏｎｓｔａｎｔｋｎ >0ｓｕｃｈｔｈａｔ‖Ｔｎｘ-Ｔｎｙ‖ ≤ｋｎ‖ｘ-ｙ‖　ｆｏｒａｌｌｘ ,ｙ∈Ｋ .ＡＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇＴｉｓｓａｉｄｔｏｂｅｕｎｉｆｏｒｍｌｙｋ＿Ｌｉｐｓｃｈｉｔｚｉａｎｉｆｋｎ =ｋｆｏｒａｌｌｎ ≥ 1 ;ｎｏ…     

Fixed Points on Two Complete and Compact Metric Spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｏｌｌｏｗｉｎｇｒｅｌａｔｅｄｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｗａｓｐｒｏｖｅｄｉｎ [1 ] .Ｔｈｅｏｒｅｍ 1　Ｌｅｔ(Ｘ ,ｄ)ａｎｄ (Ｙ ,ρ)ｂｅｃｏｍｐｌｅｔｅｍｅｔｒｉｃｓｐａｃｅｓ,ｌｅｔＴｂｅａｍａｐｐｉｎｇｏｆＸｉｎｔｏＹａｎｄｌｅｔＳｂｅａｍａｐｐｉｎｇｏｆＹｉｎｔｏＸｓａｔｉｓｆｙｉｎｇｔｈｅｉｎｅｑｕａｌｉｔｉｅｓρ(Ｔｘ,ＴＳｙ) ≤ｃｍａｘ ｄ(ｘ ,Ｓｙ) ,ρ(ｙ,Ｔｘ) ,ρ(ｙ,ＴＳｙ) ,ｄ(Ｓｙ ,ＳＴｘ) ≤ｃｍａｘ ρ(ｙ ,Ｔｘ) ,ｄ(ｘ,Ｓｙ) ,ｄ(ｘ ,ＳＴｘ)…     

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…     

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].     

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…     

Fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces and its applications

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     

Pansymmetry and fixed pansystems theorems

In this paper, we continue the research of fixed pansystems theorems presented in ref [1], and discuss the existence, the structure and the number of fixed subsets.     

Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem

This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.