Related papers: Fixed points of orientation-preserving full transf…
Following the author's previous works, we continue to consider the problem of counting the number of affine conjugacy classes of polynomials of one complex variable when its unordered collection of holomorphic fixed point indices is given.…
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to…
Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…
A permutation $\sigma$ describing the relative orders of the first $n$ iterates of a point $x$ under a self-map $f$ of the interval $I=[0,1]$ is called an \emph{order pattern}. For fixed $f$ and $n$, measuring the points $x\in I$ (according…
Let $\Delta ^{2}$ be a ball in the complex vector space $\mathbb{C}^{2}$ centered at the origin, let $f:\Delta ^{2}\to \mathbb{C}^{2}$ be a holomorphic mapping$,$ with $f(0)=0$, and let $M$ be a positive integer. If the origin 0 is an…
In the case when $X$ is a sofic shift and $\phi : X \to X$ is a homeomorphism such that $\phi^2 = \text{id}_X$ and $\phi \sigma_X = \sigma_X^{-1} \phi$, the number of points in $X$ that are fixed by $\sigma_X^m$ and $\sigma_X^n \phi$,…
In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions.…
Let $ \mathcal{I}_n$ be the symmetric inverse semigroup on $X_n = \{1, 2, \ldots , n\}$. Let $\mathcal{OCI}_n$ be the subsemigroup of $\mathcal{I}_n$ consisting of all order-preserving injective partial contraction mappings, and let…
The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani,…
Let $\alpha(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in the $p$-random subset of $\mathbb{F}_q^d$. In this note, we determine the order of magnitude of $\alpha(\mathbb{F}_q^{3},p)$ up to a…
The stage of evolution is the population of reproducing individuals. The structure of the population is know to affect the dynamics and outcome of evolutionary processes, but analytical results for generic random structures have been…
We show that Han's bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation $\pi$ with a cyclic major code $(s_1, s_2, ..., s_n)$ to…
In this paper, we consider the monoid $\mathcal{PIO}_{n}$, of all partial order-preserving transformations on a chain with $n$ elements whose domains and ranges are intervals, along with its submonoid $\mathcal{PIO}_{n}^-$ of…
We study the discrete dynamics of standard (or left) polynomials $f(x)$ over division rings $D$. We define their fixed points to be the points $\lambda \in D$ for which $f^{\circ n}(\lambda)=\lambda$ for any $n \in \mathbb{N}$, where…
Let $X$ be an algebraic variety over a finite field $\bF_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over $\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer…
The \textit{order of appearance} $ z(n) $ of a positive integer $ n $ in the Fibonacci sequence is defined as the smallest positive integer $ j $ such that $ n $ divides the $ j $-th Fibonacci number. A \textit{fixed point} arises when, for…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
We investigate the structure of fixed point sets of self-embeddings of models of arithmetic. In particular, given a countable nonstandard model M of a modest fragment of Peano arithimetic, we provide complete characterizations of (a) the…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
Despite the recent progress in genome sequencing and assembly, many of the currently available assembled genomes come in a draft form. Such draft genomes consist of a large number of genomic fragments (scaffolds), whose order and/or…