A new invariance identity and means

2018/07/12 by Jimmy Devillet, Devillet, Jimmy, Janusz Matkowski +1
Mathematics · #26A18 #26E60 #39B12 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.1807.04811

openalex publication_date 2018/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The invariance identity involving three operations D_f,g:X× X→ X of the form D_f,g( x,y) =( f∘ g) ^-1( f( x) ⊕ g( y) ) , is proposed. The connections of these operations with means is investigated. The question when the invariance equality admits three means leads to a composite functional equation. Problem to determine its continuous solutions is posed.

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