Fixed pansystems theorems and pansystems logic conservation of chaos

The study of nonlinear problems was developed in works ^[1,2] by means of the pansystems methodology (PM) which does not need the condition related to differential manifolds and linear space. In work [2], within the framework of PM, we proved that study of panchaos, panattractor and strange panattractor can be transformed conditionally into some forms of fixed subsets. As a continuation of work [2], we now research the pansystems logic conservation of panchaos, panattractor, strange panattractor and some other fixed subsets.     

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.     

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.     

An approach on fixed pansystems theorems: Panchaos and strange panattractor

The investigations about chaos, attractor and strange attractor are main subjects in nonlinear analysis. Under the framework of pansystems methodology, reference [1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omitted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansystems operators. This paper continues the investigation of [1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.The authors appreciate Associate Research Fellow Qin Guo-guang for his discussion on related problems.     

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.     

Fixed point theorems for fuzzy mappings

Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation. This paper pressents some new fixed point theorems for fuzzy mapping, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [1].     

Fixed point theorems in probabilistic inner product spaces

The purpose of this paper is to introduce a new maditying detinition for probabilistie inner product space, and to establish seveeral new fixed point theorems for mappings on such kind of spaces, As an example of applications. we utilize the results of this paper to study the existence and uniqueness of solution of Uryson’s integral equation in IV.     

Fixed point theorems of random set-valued mappings and their applications

In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4–7, 9, 11–17].     

Fixed point theorems for fuzzy mappings (II)

This paper presents some new fixed point theorems for fuzzy mappings. The results given in this paper improve and extend some recent results of [1, 4, 5].Communicated by Zhou Mo-ren     

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.     

Fixed point theorems of local contraction mappings on menger spaces

In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

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Some pansystems studies on panchaos and strange panattractor

Paper [1] discussed the relations among panchaos and strange panattractor and pansystems operators. Paper [2] gave the applications of the fixed-point pansystems theorems to these typical nonlinear problems. In this paper, we firstly present several concepts: increasing relation, maximal panchaos, etc., and discuss the relations among them. We also discuss the problems when two increasing relations have the same panchaos and when panchaos of g is panchaos of g^t as well.     

The pansystems view of prediction and blow-up of fluid

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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.     

Section theorems,coincidence theorems and intersection theorems on H-spaces with applications

The purpose of this paper is to study the section theorems, coincidence theorems and intersection theorems on H-spaces. As a way of application, we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities. The results presented in this paper improve and extend the corresponding results in [1, 3, 5, 6, 8, 9, 12, 14,15, 17]     

A new pansystems research about binary relation’s transitivity

Because of the great needs both for the research of pansystem mathematics and for the analysis of general things’ mechanism, this paper discusses the binary relation’s transitivity confined to multirelation. The so-called “g-transitivity” a completely new concept about transitivity—is introduced and its basic properties are investigated. The study shows that it is not only g-transitivity a generalization of traditional transitivity, quasi-transitivity, semi-order, quasi-order and other panorder, but also includes many important concepts such as closenss, convexity, topology, duality as its special cases.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅱ)

Forming a connecting link between what goes before and comes after,this papersummarizes the general framework of pansystems methodology and related mathematicalmodelling of fundamental concepts including generalized systems,structure,function,entirety principle of system,pansystems relations,pantransformations,panderivatives,pansymmetries,generalized quantization,etc.