Fixed points of condensing functions

Fixed Points of Condensing Multivalued Maps in Topological Vector Spaces

The Schauder conjecture that every continuous single-valued map from a compact convex subset of a topological vector space into itself has a fixed point was stated in [12, Problem 54]. In a recent year, Cauty [2] gave a positive answer to this question by a very complicated approximation factorization. Very recently, Dobrowolski [3] established Cauty’s proof in a more accessible form by using t...

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...

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...

Cycles and Fixed Points of Happy Functions

Let N = {1, 2, 3, · · · } denote the natural numbers. Given integers e ≥ 1 and b ≥ 2, let x = ∑n i=0 aib i with 0 ≤ ai ≤ b − 1 (thus ai are the digits of x in base b). We define the happy function Se,b : N −→ N by