Equality and comparison of generalized quasiarithmetic means

2024/12/10 by Zsolt Páles, Paweł Pasteczka, Páles, Zsolt +1 · 1 citation
Mathematics · #26D15 #26E60 #39B62 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2412.07315

openalex publication_date 2024/12/10 · openalex created_date 2024/12/12 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to extend the definition of quasiarithmetic 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 quasiarithmetic means. The comparability and equality problems of generalized quasiarithmetic 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 quasiarithmetic mean.

Cited by

• Hölder- and Minkowski-type inequalities for generalized quasi-arithmetic means

Related

• Equality problem for generalized quasiarithmetic means generated by discontinuous strictly monotonic functions
• Characterizations of the equality of two-variable generalized\n quasiarithmetic means
• On the σ-balancing property of multivariate generalized quasi-arithmetic means
• Hölder- and Minkowski-type inequalities for generalized quasi-arithmetic means
• Characterization of quasi-arithmetic means without regularity condition