Common fixed point theorems for expansion mappings in various spaces

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. In the memory of 65^th birthday anniversary of his Father Late Sh. Ram Phool Sharma     

Fuzzy度量空间中的单值映射的Caristi型不动点定理

本文采用Ｋａｌａｖａ和Ｓｅｉｋｋａｌａ的模糊度量空间定义，利用文（７）中建立的亚度量簇生成空间理论，研究了Ｆｕｚｚｙ度量空间中的单值映射的Ｃａｒｉｓｔｉ型不动点定理以及它在Ｍｅｎｇｅｒ概率度量空间中的应用。     

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. Next, by using these results, some new fixed point theorems on generalized (complete) algebraic cone metric spaces are proved and an example is given. As a consequence, the main results generalize the corresponding results in complete algebraic cone metric spaces and generalized complete metric spaces.     

90年代的广义度量空间理论

广义度量空间理论是一般拓扑学研究的重要课题。本文综述了90年代广义度量空间理论的成就，分析了它的主要研究课题，所取得的重要结果是国内学者在该方向的贡献。     

On an equivalence of topological vector space valued cone metric spaces and metric spaces

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied by Du (2010) [14] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper, we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable, prove a completion theorem, and also obtain some more results in topological vector space valued cone normed spaces.     

Conditions of regularity in cone metric spaces

In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included.     

Fixed point theory for generalized contractions in cone metric spaces

In this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942-2949].     

复值度量空间中F-压缩映射的叠合点

将F-压缩的概念从度量空间推广到复值度量空间中,并引进F-拟压缩的概念.说明了每个F-压缩是F-拟压缩,但反之不真.运用序列逼近的方法,对两个满足某种F-压缩条件的映射,证明了 一些叠合点结果,同时得到了一些不动点结果,这些结果推广了 Wardowski的结果.给出了几个说明性例子以突出这种推广.     

N个度量空间上的相关不动点的注记

得到了 n个度量空间上的相关不动点的几个结果 .     

Best and coupled best approximation theorems in abstract convex metric spaces

In this paper, we first give a best approximation theorem in abstract convex metric spaces. As applications, we then derive some best and coupled best approximations and coupled coincidence point results in normed spaces and hyperconvex metric spaces.     

Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces

Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by Huang and Zhang [L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive maps, J. Math. Anal. Appl. 332 (2007) 1467–1475] for cone metric spaces and by Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (1) (2007) 132–139] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above.     

度量空间中拟对称映射与拟双曲一致域的研究

本文主要考虑度量空间中拟双曲一致域与拟对称映射之间的关系，并证明了度量空间中拟双曲一致域在拟对称映射下仍然是保持不变的.     

完备和紧度量空间中的不动点

利用实函数性质,建立了两类度量空间中的几个不动点定理,推广了Fisher的有关定理。     

A Class of Metric Spaces Which Do Not Coarsely Contain Expanders

In this paper, a class of metric spaces which include Hilbert spaces and Hadamard manifolds are defined. And the expanders cannot be coarsely embedded into this class of metric spaces are proved.     

Common fixed point theorems for hybrid pairs of maps in fuzzy metric spaces

The purpose of this paper is to introduce the notion of common limit range property (CLR property) for two hybrid pairs of mappings in fuzzy metric spaces, and we prove common fixed point theorems using (CLR) property for these mappings with implicit relation. Our results extend some known results to multi-valued arena. Also, we prove common fixed point theorem in fuzzy metric spaces satisfying an integral type.     

Plasticity in metric spaces

In this paper we examine the properties of EC-plastic metric spaces, spaces which have the property that any noncontractive bijection from the space onto itself must be an isometry.     

Approximation of Metric Spaces by Partial Metric Spaces

Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.     

G-锥度量空间中压缩映射的不动点定理

给出了G-锥度量空间的概念,利用迭代法探究了G-锥度量空间中压缩映射不动点定理,证明了在G-锥度量空间中锥没有正规性的条件下压缩映射存在唯一不动点.     

Simultaneous metric projection onto closed sets

We examine simultaneous metric projection by closed sets in a class of ordered normed spaces. First, we study simultaneous metric projection onto downward and upward sets and separation properties of these sets. The results obtained are used for examination of simultaneous metric projection by arbitrary closed sets, and we examine the minimization of the distance from a bounded set to an arbitrary closed set in a class of ordered normed spaces.     

锥度量空间的若干拓扑性质

讨论锥度量空间的一些拓扑性质．主要讨论锥度量空间的邻域,开集和拓扑结构,以及锥度量空间中序列的收敛性．