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

Generalized fractal transforms and self-similar objects in cone metric spaces / H. Kunze, D. La Torre, F. Mendivil, E.R. Vrscay. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 64:6(2012), pp. 1761-1769.

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

D. La Torre
Secondo
;
2012

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
Cone metric space ; Completeness ; Contractivity ; Self-similarity ; Digital image analysis
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/05 - Analisi Matematica
2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/177547
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