Related papers: On local fixed or periodic point properties

We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$…

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…

In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.

We establish the existence of a common fixed point for mappings that satisfy and extend the F-contraction condition. To support our findings, we present pertinent definitions and properties associated with F-contraction mappings.…

Let B be any Lp space for p in (1,infty) or any Banach space isomorphic to a Hilbert space, and k be a nonnegative integer. We show that if n is at least 4, then the universal lattice Gamma =SL_n (Z[x1,...,xk]) has property (F_B) in the…

We propose the notions of uniform local weak o-minimality and $*$-local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In…

The main result of this paper is to show that for any compact space $X$ and any family $\{f_\alpha \colon \alpha< 2^\kappa, f_\alpha \colon X \stackrel{onto}{\longrightarrow} \beta \kappa\}$ of open mappings there exists a point $x \in X$…

The aim of this paper is to provide characterizations of a Meir-Keeler type mapping and a fixed point theorem for the mapping in a metric space endowed with a transitive relation.

Let p be a saddle fixed point for an orientation-preserving surface diffeomorphism f admitting a homoclinic point q. Let V be an open 2-cell bounded by a simple loop formed by two arcs joining p to q lying respectively in the stable and…

Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic…

We add to our knowledge of the approximate fixed point property (AFPP) in digital topology. We show that a digital image that is a tree has the AFPP. Given two digital images (X, \kappa) and (Y, \lambda) that have the approximate fixed…

We give several simple and easy complements to our recent paper on $C^*$-algebras with the lifting property (LP in short). In particular we observe that the local lifting property (LLP in short) associated to the class of max-contractions…

In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f…

We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows that the reflexive closure of any finite set of such…

The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…

Property($M$) in separable Banach spaces has played an important role in metric fixed point theory. This paper explores some of the Banach space properties that can be associated with Property($M$) and Property($M^*$).

We define a locally convex space $E$ to have the $Josefson$-$Nissenzweig$ $property$ (JNP) if the identity map $(E',\sigma(E',E))\to ( E',\beta^\ast(E',E))$ is not sequentially continuous. By the classical Josefson-Nissenzweig theorem,…

In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…

A space $Y$ is called an extension of a space $X$ if $Y$ contains $X$ as a dense subspace. An extension $Y$ of $X$ is called a one-point extension of $X$ if $Y\backslash X$ is a singleton. P. Alexandroff proved that any locally compact…