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].     

GENERAL RANDOM FIXED POINT THEOREM AND ITS APPLICATIONS

In this paper,we obtain a general random fixed point theorem which generalizes the main results of Engle[4,7] and Bocsan[8]. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods[1,4,5-13] can be proved by using out general theorem (Theorem 1 and Corollaries 1 and 2). Finally,we indicate some possible applications of our results to nonlinear random integral and differential equations.     

SET-VALUED CARISTI’S FIXED POINT THEOREM AND EKELANDS VARIATIONAL PRINCIPLE

This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and thin set-valued Caristi’s fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].     

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.     

NEW VERSION OF KKMTHEOREM IN PROBABILISTIC METRIC SPACES WITH APPLICATIONS

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Some coincidence theorems of set-valued mappings

Browder^[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder’s results in several aspects. Recently, H.M. Ko and K.K. Tan^[2,3] generalized Browder’s theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].     

On the equations of age-dependent population dynamics

The aim of this work is to give a direct and constructive proof of existence and uniqueness of a global solution to the equations of age-dependent population dynamics introduced and considered by M. E. Gurtin & R. C. MacCamy in [3]. The linear theory was developed by F. R. Sharpe & A. J. Lotka [10] and A. G. McKendrick [8] (see also [1], [9]) and extended to the nonlinear case by M. E. Gurtin & R. C. MacCamy in [3] (see also [4] [5] [6]). In [3], the key of the proof of existence and uniqueness was to reduce the problem to a pair of integral equations. In fact, as we shall see, the problem can also be solved by a simple fixed point argument. To outline more clearly the ideas of the proof, we will first discuss the setting and the resolution of the linear case, and then we will generalize the results of [3].     

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].     

Criteria for the existence of solutions to random integral and differential equations

In [1], we proved a general rondom fixed point theorem and gave some applications. In this paper, we shall give further applications of the theorem. We first obtain a rondom Darbo’s fixed point theorem, using the theorem, we give the criteria for the existence of solutions under compactness hypotheses to nonlinear rondom volterra integral equations and the Cauchy problem of nonlinear rondom differential equations. Our theorems improve andgeneralize some main results of Lakshmikanthem^[2], Vaughn^[3,4] as well as De Blasi and Myjak^[5].     

A note on a theorem of Tas, Telci and Fisher

I.IntroductionInarecentpaperTas,TelciandFisherlZ],obtainedthefollowingimprovedandgeneralizedversionofafixedpointtheoremofSharmaandSahulll:TheoremALet.A,B,SandTbeselfmappillgsonacompletemetricspace(X,ti,satisfyingA(X)GT(X)andB(X)GS(X)(l.l)[d(Ax,By)]2$Clmax{[d(Sx,Ax)]',[d(Ty,By)jZ,[d(Sx,Ty)]2} cd.max{d(Sx,Ax).d(Sx,By),d(Ax,Ty).d(By,Ty)} c,.d(Sx,By).d(Ty,As)(1.2)t'orallx,yinX,whereof,cZ,c3>0,of 2c2相似文献   

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     

Singular perturbation of general boundary value problem for nonlinear differential equation system

I.IntroductionAllphysicalsystemsarenonlineartosomeextent.Actually,Lineal.systemisimaginarymodelwherenonlinearfactorisomittedinnonlinearsystem.Insolvingtheautocontl'ol,nonlinearoscillationtheory,theboundarystagnationproblenloffluidIncchanicsandsollleproblemsofsemi-conducttheoryandquantummechanicsetc'.weOnlyncedtosolvethefollowingproblem,whichisnonlineardifferentialequationsystemwithtilesll,allparanletel'inhighestorderderivativeandnonlinearboundaryconditions.whereE>0isasmallparameter,teR,x,fi…     

On the trajectories of a mass point on a rotating surface

N. E. Zhukovskii proposed a special method [1] for determining the trajectories of amass point (particle) on a plane in the field of potential forces. In [2], this method was generalized to the case of particle motions on curvilinear surfaces. In the present paper, this method is generalized to the case in which the surface, together with the field of potential forces, rotates about a fixed axis. Several examples are considered.     

New integrable problems of motion of a rigid body with a particle oscillating or bouncing in it

Some qualitative aspects of the problem of motion about a fixed point of a rigid body with a particle moving in it in a prescibed (sinusoidal) way was treated in [1–3]. The mechanical system comprised of a rigid body containing an internal mass that moves along a fixed line in the body was considered in several works [4–5]. Recently, an integrable case of this system was found, in which the body is dynamically axisymmetric and moves under no external forces while the particle moves on the axis of dynamical symmetry under the action of Hooke's force to the fixed point [5].In the present note we introduce a more general integrable case in which the particle moves on the axis of dynamical symmetry and is subject to an arbitary conservative force that depends only on the distance from the fixed point. Separation of variables is accomplished and the solution is reduced to quadratures. As a special version of this problem, the case when the particle bounces elastically between two points is briefly discussed.     

Fixed point indexes and its applications to nonlinear integral equations modelling infectious diseases

In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed, and some sufficient conditions for the fixed point index to be equal to 1 or 0 are given. Moreover, a general fixed point theorem of expansions and compressions for cone is obtained, which generalizes and improves the corresponding results of [3,8,9]. As an application, we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.Project supported by National Natural Science Foundation of China.     

Oscillations of a body filled with a viscous fluid

The oscillations of a physical pendulum containing a spherical cavity filled with an incompressible viscous liquid were discussed in [1]. In this paper we consider the mote general problem of the motion of an axially symmetric solid with a spherical cavity filled with an incompressible viscous fluid and moving about a fixed point. It is assumed that the center of the cavity and the fixed point lie on the axis of symmetry of the body.     

Boundary value problems for second order delay differential equations

In this paper,using a fixed point principle and existence principle given in[1],westudy the boundary value problems for second order differential equations.Some newexistence results are obtained.     

THE UNIQUENESS AND EXISTENCE OF SOLUTION OF THE CHABACTERISTIC PROBLEM ON THE GENERALIZED KdV EQUATION

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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].     

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].