A fixed point theorem for a family of mappings in a fuzzy metric space

In this paper we give a common fixed point theorem for a family of mappings of a G-complete fuzzy metric space (X, M, *) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space (X, d) into itself. Supported by University of Palermo.     

An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1].     

概率度量空间中若干新的不动点定理*

本文提出了Z-M-PN空间的概念,在概率度量空间中我们得到了若干新的不动点定理。同时,一些着名的不动点定理在概率度量空间中得到了推广,诸如:Schauder不动点定理、郭大钧不动点定理和Petryshyn不动点定理被推广到M-PN空间;Altman不动点定理被推广到Z-M-PN空间。     

A fixed point theorem in hyperconvex spaces

In this article we prove a new fixed point theorem for hyperconvex metric spaces. The significance of our result will be clarified by suitable examples and a comparison with earlier fixed point theorems for hyperconvex spaces. In particular, we prove that the space \Bbb Rⁿ\Bbb R^n with the metric "river" or with the radial metric is hyperconvex.     

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.     

Note on “Coupled fixed point theorems for contractions in fuzzy metric spaces”

In the paper “Coupled fixed point theorems for contractions in fuzzy metric spaces” by Sedghi et al. [S. Sedghi, I. Altun, N. Shobec, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72 (2010) 1298-1304], a coupled common fixed point result was presented. However, our purpose is to show that this result and its proof are false. We give a counterexample and also explain how to correct this result. As a modification, we state and prove a coupled fixed point theorem under some hypotheses of fuzzy metric and t-norm.     

On Fuzzy Metric Space

In this paper we prove a common fixed point theorem for three mappings in fuzzy metric space and then extend this result to fuzzy 2 and 3-metric spaces. Our theorem is an extension of result of Fisher [12], to fuzzy metric spaces.AMS Subject Classification (1990): 47H10, 54H25     

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.     

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.     

Fuzzy n-cell numbers and the differential of fuzzy n-cell number value mappings

In this paper, we give the definition of a special kind of n-dimension fuzzy numbers, fuzzy n-cell numbers, discuss their operations and representation theorems, define a complete metric on the fuzzy n-cell number space and prove that the metric is equivalent to the supremum metric derived by the Hausdorff metric between the level sets of the n-dimension fuzzy numbers, and obtain an embedding theorem of the fuzzy n-cell number space (isometrically embeds it into a concrete Banach space). We also consider the differential of the fuzzy mappings from an interval into the fuzzy n-cell number space by using the embedding theorem.     

Fixed points of fuzzy contractive and fuzzy locally contractive maps

We establish some fixed point theorems for fuzzy contractive and fuzzy locally contractive mappings on a compact metric space with the d_∞-metric for fuzzy sets. Our results generalized well-known classical results of Edelstein.     

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.     

On fuzzy metric spaces

In this paper we introduce the concept of a fuzzy metric space. The distance between two points in a fuzzy metric space is a non-negative, upper semicontinuous, normal and convex fuzzy number. Properties of fuzzy metric spaces are studied and some fixed point theorems are proved.     

<Emphasis Type="Italic">G</Emphasis>-completeness and <Emphasis Type="Italic">M</Emphasis>-competeness in fuzzy metric spaces: A note on a common fixed point theorem

In the recent paper of this journal [7], a common fixed point theorem in G-complete fuzzy metric spaces under the t-norm Min was proved. We show that this theorem actually holds in more general situations.     

L-凸度量空间中的GLKKM定理及其应用

引进了L-凸度量空间的概念,在L-度量空间中建立了GLKKM映射的GLKKM定理．作为应用,获得了一个Browder不动点定理．     

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.     

关于模糊预度量空间中的三角不等式

在L，R为一般三角模时，给出在模糊预一度量空间中三角不等式成立的一个必要条件，并用其给出模糊度量空间的一个不动点定理。     

New cone fixed point theorems for nonlinear multivalued maps with their applications

In this paper, we first establish some new types of fixed point theorems for nonlinear multivalued maps in cone metric spaces. From those results, we obtain new fixed point theorems for nonlinear multivalued maps in metric spaces and the generalizations of Mizoguchi–Takahashi’s fixed point theorem and Berinde–Berinde’s fixed point theorem. Some applications to the study of metric fixed point theory are given.     

Suzuki?s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], Nieto and Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239]. We deduce, also, common fixed point results for two self-mappings. Moreover, using our results, we obtain a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends Suzuki?s characterization of metric completeness.     

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。