Fixed points and proximate 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...

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...

Blowup and Fixed Points

Blowing up a point p in a manifold M builds a new manifold M̂ in which p is replaced by the projectivization of the tangent space TpM . This well–known operation also applies to fixed points of diffeomorphisms, yielding continuous homomorphisms between automorphism groups of M and M̂ . The construction for maps involves a loss of regularity and is not unique at the lowest order of differentiabili...

Approximating fixed points of generalized nonexpansive mappings

Demonic Fixed Points

We deal with a relational model for the demonic semantics of programs. The demonic semantics of a while loop is given as a fixed point of a function involving the demonic operators. This motivates us to investigate the fixed points of these functions. We give the expression of the greatest fixed point with respect to the demonic ordering (demonic inclusion) of the semantic function. We prove th...