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

Authors:
H. Kunze;D. La Torre;F. Mendivil;E. R. Vrscay
Affiliations:
Department of Mathematics and Statistics, University of Guelph, Canada;Department of Economics, Business and Statistics, University of Milan, 20122 Milano, Italy;Department of Mathematics and Statistics, Acadia University, Canada;Department of Applied Mathematics, University of Waterloo, Canada
Venue:
Computers & Mathematics with Applications
Year:
2012

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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.