Digital fixed points, approximate fixed points, and universal functions

Laurence Boxer, Ozgur Ege, Ismet Karaca, Jonathan Lopez, Joel Louwsma

Abstract

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 approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).

Keywords

digital image; digitally continuous; digital topology; fixed point

Subject classification

55M20; 55N35

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