Work

Equality and comparison of generalized quasi-arithmetic means

Year: 2025

Type: article

Abstract: The purpose of this paper is to extend the definition of quasi-arithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one. We establish the properties of such means and compare them to the analogous properties of standard quasi-arithmetic means. The comparability and equality problems of generalized quasi-arithmetic are also solved. We also provide an example of a mean which, depending on the underlying interval or on the number of variables, could be or could not be represented as a generalized quasi-arithmetic mean.

Source: Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

DOI: 10.1007/s13398-025-01813-1

Authors: Zsolt Páles, Paweł Pasteczka

Institutions: University of Debrecen, University of Rzeszów

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Debreceni Egyetem, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal