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Reducible means

Reducible means A n variables mean M is said to be reducible in a certain class of means $$\mathcal {N}$$ N when M can be represented as a composition of a finite number $$M_{0},\ldots ,M_{r}$$ M 0 , … , M r of means belonging to $$\mathcal {N}$$ N , being less than n the number of variables of every $$M_{i}$$ M i . In this paper, a basic classification of reducible means is developed and the notions of S-reducibility, a type of analytically decidible reducibility, and of complete reducibility of a mean are isolated. Several applications of these notions are presented. In particular, a continuous and scale invariant weighting procedure defined on a class $$\mathcal {M}_{2}$$ M 2 of two variables means is extended without losing its properties to the class of reducible means in $$\mathcal {M}_{2}$$ M 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0156-8
Publisher site
See Article on Publisher Site

Abstract

A n variables mean M is said to be reducible in a certain class of means $$\mathcal {N}$$ N when M can be represented as a composition of a finite number $$M_{0},\ldots ,M_{r}$$ M 0 , … , M r of means belonging to $$\mathcal {N}$$ N , being less than n the number of variables of every $$M_{i}$$ M i . In this paper, a basic classification of reducible means is developed and the notions of S-reducibility, a type of analytically decidible reducibility, and of complete reducibility of a mean are isolated. Several applications of these notions are presented. In particular, a continuous and scale invariant weighting procedure defined on a class $$\mathcal {M}_{2}$$ M 2 of two variables means is extended without losing its properties to the class of reducible means in $$\mathcal {M}_{2}$$ M 2 .

Journal

The Journal of AnalysisSpringer Journals

Published: Dec 13, 2018

References