Related papers: A note on the relation between fixed point and orb…
In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Let C be a nonempty, bounded, closed, and convex subset of a Banach space X and $T : C \rightarrow C$ be a monotone asymptotic nonexpansive mapping. In this paper, we investigate the existence of fixed points of T. In particular, we…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
A general relation is derived for the action difference between two fixed points and a phase space area bounded by the irreducible component of a heteroclinic tangle. The determination of this area can require accurate calculation of…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces…
This paper advances a general proposal for testing non-standard cosmological models by means of observational relations of cosmological point sources in some specific waveband, and their use in the context of the data provided by the galaxy…
In this paper we consider a one dimensional liner piecewise-smooth discontinuous map. It is well known that stable periodic orbits exist in this type of map for a specific parameter region. It is also known that the corresponding…
The purpose of this paper is twofold. First we study bifurcations of connected sets of critical orbits of some invariant functional from a given family of critical orbits. We use techniques of equivariant bifurcation theory to obtain a…
We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…
In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…
We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.
The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…
We explore a combinatorial bijection between two seemingly unrelated topics: the roots of irreducible polynomials of degree $m$ over a finite field $F_p$ for a prime number $p$ and the number of points that are periodic of order $m$ for a…
We study maps on the set of permutations of n generated by the R\'enyi-Foata map intertwined with other dihedral symmetries (of a permutation considered as a 0-1 matrix). Iterating these maps leads to dynamical systems that in some cases…
We discuss two concepts of metric and linear connections in noncommutative geometry, applying them to the case of the product of continuous and discrete (two-point) geometry.
The purpose of this short communication is to make some observations on the connections between various existing formulas of counting the number of sublattices of a fixed index in an $n$-dimensional lattice and their connection with the…