Some mapping theorems for extensional dimension

A fixed point theorem for contractive mappings that characterizes metric completeness

Inspired by the work of Suzuki in [Proc. Amer. Math. Soc. 136 (2008), 1861--1869] we prove a fixed point theorem for contractive mappings that generalizes a theorem of Geraghty in [Proc. Amer. Math. Soc., 40 (1973), 604--608] and characterizes metric completeness.

广义Kannan型映射的不动点定理

Fixed point theorem for generalized Kannan type mappings

本文提出度量空间中广义Kannan型映射，证明其不动点定理，并借助渐近正则性与连续性条件将结论推广到更广泛的映射类及非完备度量空间。

收缩三角形周长的映射的不动点定理

Fixed point theorem for mappings contracting perimeters of triangles

本文研究度量空间中收缩三角形周长的新映射，证明其连续性及不动点定理，将 Banach 不动点定理作为推论，并构造了非收缩映射的例子。

A remark on a theorem of Iliadis concerning isometrically containing mappings

In this paper we give an alternative proof and a refinement of a recent result of S.D.Iliadis concerning isometrically containing mappings. We address also a recent result by A.I.Oblakova.

On discrete and semimetric fixed point theorems for nonexpansive mappings

This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.

Fixed Point Theorems for Set-Valued Mappings on TVS-Cone Metric Spaces

In the context of tvs-cone metric spaces, we prove a Bishop-Phelps and a Caristi's type theorem. These results allow us to prove a fixed point theorem for $(δ, L)$-weak contraction according to a pseudo Hausdorff metric defined by means of a cone metric.

On a Fixed Point Theorem for a Cyclical Kannan-type Mapping

This paper deals with an extension of a recent result by the authors generalizing Kannan's fixed point theorem based on a theorem of Vittorino Pata. The generalization takes place via a cyclical condition.

Chatterjea不动点定理的一个至多具有两个不动点的三点推广

A three point extension of Chatterjea's fixed point theorem with at most two fixed points

本文提出Chatterjea型映射的三点类似物，证明其与原始映射不同，建立广义映射的不动点定理并揭示与其他映射类型的联系，且在非完备度量空间中也得到两个不动点定理。

Fixed point theorems for $α$--contractive mappings of Meir--Keeler type and applications

In this paper, we introduce the notion of $α$--contractive mapping of Meir--Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems.

An Open Mapping Theorem

It is proved that any surjective morphism $f: \mathbb{Z}^κ\to K$ onto a locally compact group $K$ is open for every cardinal $κ$. This answers a question posed by Karl Heinrich Hofmann and the second author.

关于Banach和Edelstein不动点定理的三点推广

On three-point generalizations of Banach and Edelstein fixed point theorems

本文提出并研究度量空间上更一般的$(F,G)$-收缩映射，证明其不动点定理，并推广Edelstein意义下收缩三角形周长的映射的不动点定理。

广义Chatterjea型映射的不动点定理

Fixed point theorem for generalized Chatterjea type mappings

本文提出度量空间中广义Chatterjea型映射（三点类比），证明其可间断且包含原类，并给出不动点定理。

On the Closed Graph Theorem and the Open Mapping Theorem

Let $E,F$ be two topological spaces and $u:E\rightarrow F$ be a map. \ If $F$ is Haudorff and $u$ is continuous, then its graph is closed. \ \ The Closed Graph Theorem establishes the converse when $E$ and $F$ are suitable objects of topological algebra, and more specifically topological groups, topological vector spaces (TVS's) or locally vector spaces (LCS's) of a special type. The Open Mapping Theorem, also called the Banach-Schauder theorem, states that under suitable conditions on $E$ and $F,$ if $ v:F\rightarrow E$ is a continuous linear surjective map, it is open. \ When the Open Mappin…

$b$-类度量空间中两个映射的公共不动点定理

Common fixed point theorems for two mappings in $b$-metric-like spaces

研究 $b$-类度量空间中两个自映射的公共不动点存在性，给出了保证其拥有公共不动点的若干条件。

An open mapping theorem for finitely copresented Esakia spaces

We prove an open mapping theorem for the topological spaces dual to finitely presented Heyting algebras. This yields in particular a short, self-contained semantic proof of the uniform interpolation theorem for intuitionistic propositional logic, first proved by Pitts in 1992. Our proof is based on the methods of Ghilardi & Zawadowski. However, our proof does not require sheaves nor games, only basic duality theory for Heyting algebras.