半序概率度量空间中压缩算子的不动点定理

半序方法是研究非线性算子方程问题的主要方法之一.在概率度量空间中引入半序,并且利用半序方法研究了非线性算子的不动点问题,推广了度量空间中序压缩算子的不动点定理,获得若干新的结果.     

Menger概率度量空间中Caristi型混合不动点定理

本文在Menger概率度量空间中引进Caristi型混合不动点概念,得到两个混合不动点定理和两个集值映象序列的公共混合不动点定理,我们的定理改进和推广了Caristi不动点定理及相关的近期重要结果.     

H—度量空间中的广义KKM定理及其应用

定义了一个新的空间-H-度量空间并在H-度量空间中,得到了具有有限度量紧闭（开）值的广义H-KKM映像的广义H-KKM定理,这些定理推广了Khamsi和Yuan最近一系列结果。作为应用,还得到有限度量紧闭（开）覆盖的Ky Fan型匹配定理,不动点定理和极小极大不等式,这些结果统一和推广了近期的许多结果。     

概率度量空间在分形图理论中的应用

给出广义概率度量空间上的随机压缩映射的新定义,统一了概率度量空间中的概率压缩,E-空间中的强压缩,随机度量空间中的几乎处处压缩和均匀压缩的定义.在广义概率度量空间上给出几个新的不动点定理,将概率度量空间中的一些熟知的不动点定理作为推论得到.利用这些不动点定理,得到分形图理论中随机迭代函数系统的遍历性定理.     

拓扑空间中一些新的不动点定理

介绍了我们在不动点定理方面的一些最新结果，包括：拓扑空间中Meir-Keeler型映象的不动点定理，有序拓扑空间中增算子和多值增映射的不动点定理，拓扑空间中压缩映象的不动点定理和多值映象的公共不动点定理。甚至在通常的度量空间，所有这些结果也是新的。     

一类g-可比较算子方程的可解性定理

本文在半序度量空间中引进了g-可比较算子和耦合不动点和9-不动点这些新概念,研究了9-可比较算子的g-耦合不动点或g-不动点存在性问题,得到了几个存在性定理.所得结论推广了最近一些文献中的主要结果.     

半序概率度量空间中压缩映射序列的重合点定理

本文在概率度量空间中定义广义β-可容许映射序列这个新概念,在不同的压缩条件下,利用半序方法,得到映射序列的重合点定理,所得结论推广和改进了有关文献中的不动点定理,最后给出主要结果的一个应用.     

度量空间和锥度量空间中的若干不动点定理

给出了度量空间和锥度量空间中的若干不动点定理.利用这些不动点定理,统一并推广了度量空间和锥度量空间中的若干经典的不动点定理.     

Fuzzy度量空间上Lipschitz型自映射的公共不动点

在Fuzzy度量空间上建立了一个Lipschitz型自映射的公共不动点定理。作为应用,得到Fuzzy度量空间上Bose型和Kannan-Reich型自映射的公共不动点定理,从而统一并推广了Bose与KannanReich在度量空间上的有关结论。     

锥度量空间中扩张映射的一个新的不动点定理

为了研究完备的锥度量空间中扩张型映象不动点的存在性和唯一性问题,对满足不同条件的扩张型映象,采用不同的迭代方法,得到了锥度量空间中扩张映射的一个新的不动点定理.这些结果是度量空间中某些经典结果在锥度量空间的进一步推广和发展.     

Fixed Points of Sequence of Ćirić Generalized Contractions of Perov Type

Perov used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article, we study fixed point results for the new extensions of sequence of ?iri? generalized contractions on cone metric space, and we give some generalized versions of the fixed point theorem of Perov. The theory is illustrated with some examples. It is worth mentioning that the main result in this paper could not be derived from ?iri?’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.     

Monotone generalized contractions in partially ordered probabilistic metric spaces

In this paper, a concept of monotone generalized contraction in partially ordered probabilistic metric spaces is introduced and some fixed and common fixed point theorems are proved. Presented theorems extend the results in partially ordered metric spaces of Nieto and Rodriguez-Lopez [Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], Ran and Reurings [A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443] to a more general class of contractive type mappings in partially ordered probabilistic metric spaces and include several recent developments.     

Extension of contractive maps in the Menger probabilistic metric space

In this article, the topological properties of the Menger probabilistic metric spaces and the mappings between these spaces are studied. In addition, contractive and k-contractive mappings are introduced. As an application, a new fixed point theorem in a chainable Menger probabilistic metric space is proved.     

Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces

The probabilistic version of the classical Banach Contraction Principle was proved in 1972 by Sehgal and Bharucha-Reid [V.M. Sehgal, A.T. Bharucha-Reid, Fixed points of contraction mappings on PM spaces. Math. Syst. Theory 6, 97–102]. Their fixed point theorem is further generalized by many authors. In the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems. However, the problem to prove the probabilistic versions of the very important generalization of the Banach Contraction Principle, obtained in 1969 by Boyd and Wong [D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Am. Math. Soc. 20 (1969) 458–464], who proved the fixed point theorem for a self-mapping of a metric space, satisfying the very general nonlinear contractive condition, is unsolved in these days. Similarly, as in the metric space case, to prove a fixed point theorem for a mapping, satisfying the general probabilistic nonlinear contractive condition, it was necessary to find a new approach, substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition, introduced by Sehgal and Bharucha-Reid and further used by many authors. So, the problem to obtain a truthful probabilistic version of the Banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years. We have solved this problem in this paper.     

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.     

Edelstein's fixed point theorem in topological spaces

An extension to topological spaces of a wellknown fixed point theorem of M. Edelstein for contractive mappings on metric spaces is presented. Results based on the generalized Edelstein's theorem are also established concerning the existence of fixed points of continuous selfmaps on a topological space. As a special case a compact starshaped subset of a linear topological space is considered. The results extend the fixed point theoremsfor nonexpansive mappings on a compact metric space of L.F.Guseman, Jr. and B.C. Peters, Jr.     

概率度量空间中广义β-可容许映射的二元重合点定理及其应用

在Menger PM-空间中,引入广义β-可容许映射的概念。在不要求两映射可交换的情况下,利用迭代法,建立了广义β-可容许映射的二元重合点定理。获得了一些新的结果,推广和改进了相关文献中的不动点定理和二元重合点定理。最后,给出了主要结果的一个应用。     

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.