TL;DR
This paper introduces the concept of cancelling means within a class of partially ordered means, providing a method to identify such means for well-known classes like Hölder and Stolarsky means.
Contribution
It presents a new framework for understanding cancelling means and offers a simple method to determine them for classical mean classes.
Findings
Defined the notion of cancelling mean for partially ordered means.
Provided a method to identify cancelling means for Hölder and Stolarsky means.
Enhanced understanding of the structure of mean hierarchies.
Abstract
For a class of partially ordered means we introduce a notion of the (nontrivial) cancelling mean. A simple method is given which helps to determine cancelling means for well known classes of Holder and Stolarsky means.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematical Inequalities and Applications · Iterative Methods for Nonlinear Equations