严格集压缩映射和凝聚映射的延拓定理及应用(英文)

应用著名的Dugundji延拓定理和Urysohn引理,将Hilbert空间E中有界闭凸集D上的k-集压缩映射和聚映射延拓到全空间,并给出了其在拓扑度计算方面的应用.     

Best Proximity Point Theorems for Generalized Cyclic Contractions in Ordered Metric Spaces

In this paper, we generalized a cyclic contraction on a partially ordered complete metric space. We prove some fixed point theorems as well as some theorems on the existence of best proximity points. Our results improve and extend some recent results in the previous work.     

KKM property and fixed point theorems in metric spaces

In this paper, first part, we establish some fixed point theorems for a k-set contraction map on the nearly-subadmissible subsets of a complete metric space. The second part, we deduce a generalization of the approximate fixed point theorem for the lower semicontinuous mappings on a metric space.     

Controlled fuzzy metric spaces and some related fixed point results

In this paper, we introduce a new extension in the subject of fuzzy metric, called controlled fuzzy metric space. This notion is a generalization of fuzzy b‐metric space. Also, we prove a Banach‐type fixed point theorem and a new fixed point theorem for some self‐mappings satisfying fuzzy ψ ‐contraction condition that is more general than existing theorems. Furthermore, we establish some examples about our main results.     

Viscosity approximations by generalized contractions for resolvents of accretive operators in Banach spaces

In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.     

一类高阶非线性中立型差分方程组非振动解的存在性

研究了一类高阶非线性中立型差分方程组非振动解的存在性.利用Banach空间的压缩映象原理,获得了该方程组存在非振动解的充分条件.     

简化原理在Hilbert空间与可分Banach空间的一些应用

本文研究了简化原理在Hilbert空间与可分Banach空间中的一些应用,利用简化原理和独立随机元收敛准则获得了中分Banach空间随机级数的收缩原理和B-值随机Dirichlet级数简单收敛横坐标及一般随机整函数的增长性和值分布,将许多以Rademacher序列为系数的随机Tayor级数和随机Dirichlet级数的相关结果,推广到一般的具有独立对称分布系数的随机级数上去。     

非线性压缩算子半群的不变流

本文主要给出了Ｂａｎａｃｈ空间中非线性压缩算子半群存在不交流的充要条件，并且在Ｃ＊－代数及Ｈｉｌｂｅｒｔ空间中刻划了正非线性压缩算子半群的特征．     

Time periodic solutions of compressible Navier-Stokes equations

In this paper, we study the Navier-Stokes equations with a time periodic external force in Rn. We show that a time periodic solution exists when the space dimension n?5 under some smallness assumption. The main idea is to combine the energy method and the spectral analysis for the optimal decay estimates on the linearized solution operator. With the optimal decay estimates, we prove the existence and uniqueness of time periodic solution in some suitable function space by the contraction mapping theorem. In addition, we also study the time asymptotic stability of the time periodic solution.     

Iterative construction of fixed points

Abstract, It is proved that an Ishikawa—type iteration scheme converges to the fixed point of a generalized contraction map in a convex metric space. The class of generalized contraction maps includes all quasi—contraction maps. Our theorem generalizes some recent important known results     

Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

Equivalence of completeness and contraction property

In this paper, we consider the completeness and the contraction property in metric spaces and show that the contraction property implies Lipschitz-completeness or arcwise-completeness in a metric space. However, in a metric space, the contraction property does not imply the usual completeness. We prove that a locally Lipschitz-connected metric space has the contraction property if and only if it is Lipschitz-complete and that a locally arcwise-connected metric space is arcwise-complete if and only if has the strong contraction property.

     

Some new extensions of Banach’s contraction principle to partial metric space

In S.G. Matthews [S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183–197], the author introduced and studied the concept of partial metric space, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this work we study fixed point results for new extensions of Banach’s contraction principle to partial metric space, and we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.     

具有一类新压缩条件下自映射的不动点

本文推广了文 [6]中的压缩条件 ,并给出了度量空间中在该压缩条件下自映射的不动点存在唯一性定理     

On polynomially bounded operators acting on a Banach space

By the Von Neumann inequality every contraction on a Hilbert space is polynomially bounded. A simple example shows that this result does not extend to Banach space contractions. In this paper, we give general conditions under which an arbitrary Banach space contraction is polynomially bounded. These conditions concern the thinness of the spectrum and the behaviour of the resolvent or the sequence of negative powers. To do this we use techniques from harmonic analysis, in particular, results concerning thin sets such as Helson sets, Kronecker sets and sets that satisfy spectral synthesis.     

Fixed‐point theorem for a generalized almost Hardy‐Rogers‐type F contraction on metric‐like spaces

In this paper, we introduce some fixed‐point theorems for a generalized almost Hardy‐Rogers‐type F contraction in a metric‐like space and give an example to illustrate these main results. Moreover, we show the applications of electric circuit equations, second‐order differential equations, and fractional differential equations. Our results improve, generalize, and extend the corresponding results in literature.     

Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems

The piecewise continuous function space is an important state space in various nonlinear problems. In this paper, we establish some new fixed point theorems for the perturbed contraction operators in piecewise continuous function spaces. Our results can be applied to various integral operators. Some previous results are improved in this literature. As applications, the existence and uniqueness of solutions of impulsive anti‐periodic boundary value problems and the Lasota–Wazewska models with delays are exhibited at last two sections. Copyright © 2013 John Wiley & Sons, Ltd.     

The Cauchy problem for the dissipative Boussinesq equation

This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given.     

Fixed points of multifunctions on regular cone metric spaces

Each metric space is a regular cone metric space. We shall extend a result about Meir–Keeler type contraction mappings on metric spaces to regular cone metric spaces. Also, we shall give some results about fixed point of weakly uniformly strict p$p$-contraction multifunctions on regular cone metric spaces.     

Darbo type fixed and coupled fixed point results and its application to integral equation

We propose two new notion of contraction mappings involving measure of noncompactness in the frame work of Banach space and derive some basic Darbo type fixed and coupled fixed point results. The results are correlated with the classical Banach fixed point theorems. Further we show the applicability of obtained results to the theory of integral equations following a concrete example which illustrate the application part.