Characterizations of the equality of two-variable generalized\n quasiarithmetic means

2020/12/07 by Zsolt Páles, Páles, Zsolt, Amr Zakaria +1
Mathematics · #26B99 #39B22 #39B52 #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.2012.03588

openalex publication_date 2020/12/07 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

This paper is motivated by an astonishing result of H. Alzer and S.\nRuscheweyh published in 2001 in the Proc. Amer. Math. Soc., which states that\nthe intersection of the classes two-variable Gini means and Stolarsky means is\nequal to the class of two-variable power means. The two-variable Gini and\nStolarsky means form two-parameter classes of means expressed in terms of power\nfunctions. They can naturally be generalized in terms of the so-called\nBajraktarevi 'c and Cauchy means. Our aim is to show that the intersection of\nthese two classes of functional means, under high-order differentiability\nassumptions, is equal to the class of two-variable quasiarithmetic means.\n

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