Global Wilson–Fisher fixed points

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Global fixed points for centralizers and Morita’s Theorem

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk D that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeomorphism with infinitely many global fixed points. As another application we giv...

Digital Fixed Points, Approximate Fixed Points, and Universal Functions

A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approxima...

New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

and Applied Analysis 3 (w3) for any ε > 0, there exists δ > 0 such that p(z, x) ≤ δ and p(z, y) ≤ δ imply d(x, y) ≤ ε. A function p : X×X → [0,∞) is said to be a τ-function [5, 10, 14, 15, 27–29], first introduced and studied by Lin and Du, if the following conditions hold: (τ1) p(x, z) ≤ p(x, y) + p(y, z) for all x, y, z ∈ X; (τ2) if x ∈ X and {yn} in X with limn→∞yn = y such that p(x, yn) ≤ M...

Approximating fixed points of generalized nonexpansive mappings