Generalized fractal transforms and self-similar objects in cone metric spaces

https://doi.org/10.1016/j.camwa.2012.02.011Get rights and content
Under an Elsevier user license
open archive

Abstract

We use the idea of a scalarization of a cone metric to prove that the topology generated by any cone metric is equivalent to a topology generated by a related metric. We then analyze the case of an ordering cone with empty interior and we provide alternative definitions based on the notion of quasi-interior points. Finally we discuss the implications of such cone metrics in the theory of iterated function systems and generalized fractal transforms and suggest some applications in fractal-based image analysis.

Keywords

Cone metric space
Completeness
Contractivity
Self-similarity
Digital image analysis

Cited by (0)