TL;DR
This paper introduces a novel class of means where both the domain and the values are sets, exploring their properties, behaviors, and providing natural examples of such means.
Contribution
It presents a new type of mean that operates on sets and yields sets, expanding the concept of averaging to set-valued functions.
Findings
Characterization of properties of set-based means
Examples demonstrating natural occurrences of such means
Analysis of the behavior and properties of the new means
Abstract
We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such means.
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Taxonomy
TopicsFunctional Equations Stability Results · Optimization and Variational Analysis