Digital fixed points, approximate fixed points, and universal functions

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...

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...

Approximate fixed points of nonexpansive functions in product spaces

1 Department of Mathematics, Darmstadt University of Technology Schlossgartenstrasse 7, D-64289 Darmstadt, Germany [email protected] 2 Institute of Mathematics ”Simion Stoilow” of the Romanian Academy P.O. Box 1-462, Bucharest, Romania Currently: Department of Mathematics, Darmstadt University of Technology Schlossgartenstrasse 7, D-64289 Darmstadt, Germany leustean@mathemat...

Fixed Points of Analytic Functions

Fixed points of β - functions

The evidently supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a betafunction form the moduli space M = RP 2 where two types of phases were found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase which may be inte...