On quasi-metric aggregation functions and fixed point theorems

The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was exten...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 228; pp. 88 - 104
Main Authors: Martín, J., Mayor, G., Valero, O.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2013
Subjects:
Agglomeration
Aggregation function
Asymmetry
Asymptotic complexity analysis
Complexity
Computation
Denotational semantics
Fixed points (mathematics)
Homogeneous function
Mathematical analysis
Mathematical models
Metric
Projective [formula omitted]-contraction
Projective contraction
Quasi-metric
Recursive
Theorems
Projective contraction
Denotational semantics
Homogeneous function
Metric
Asymptotic complexity analysis
Quasi-metric
Aggregation function
Projective Φ-contraction
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was extended to the quasi-metric context in such a way that a general description of how to combine through a function a family of quasi-metrics in order to obtain a single one as output was provided by G. Mayor and O. Valero [Aggregation of asymmetric distances in Computer Science, Inform. Sci.180 (2010) 803–812]. In this paper, inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences, we have proved fixed point theorems for a new type of contractions, that we have called projective Φ-contractions, defined between quasi-metric spaces that have been obtained via the so-called quasi-metric aggregation functions. Moreover, we show that the new fixed point results are useful to discuss, on the one hand, the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and, on the other hand, to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification.
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ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2012.08.009