Results in Mathematics

, Volume 71, Issue 1–2, pp 397–410

# Explicit Solutions of the Invariance Equation for Means

Open Access
Article

## Abstract

Extending the notion of projective means we first generalize an invariance identity related to the Carlson log given in Kahlig and Matkowski (Math Inequal Appl 18(3):1143–1150, 2015), and then, more generally, given a bivariate symmetric, homogeneous and monotone mean M, we give explicit formula for a rich family of pairs of M-complementary means. We prove that this method cannot be extended for higher dimension. Some examples are given and two open questions are proposed.

## Keywords

Invariant means homogeneous means

26D15

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## Authors and Affiliations

• Janusz Matkowski
• 1
• Monika Nowicka
• 2
• Alfred Witkowski
• 2
Email author
1. 1.Faculty of Mathematics, Computer Sciences and EconometricsUniversity of Zielona GoraZielona GóraPoland
2. 2.Institute of Mathematics and PhysicsUTP University of Science and TechnologyBydgoszczPoland

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