Matkowski-Sutô type problem for conjugate arithmetic means
View/
xmlui.dri2xhtml.METS-1.0.item-citation: Rocznik Naukowo-Dydaktyczny. 2000, Z. 204, Prace Matematyczne 17, s. 89-100
xmlui.dri2xhtml.METS-1.0.item-iso: en
Date: 2000
Metadata
Show full item recordAbstract
Let I ⊂ R be an open interval and let CM(I) denote the set of all continuous and strictly monotonie real functions on I. For ϕ ϵ CM(I)
we define A[*][ϕ](x,y) := ϕ[-1](ϕ(x) + ϕ(y) - ϕ(x+y/2) for all x,y ϵ I, which is called a conjugate arithmetic mean on I. In this paper we
solve the functional equation A[*][ϕ](x,y) + A[*][ϕ](x,y) = x + y for all x,y ε I, where ϕ,ψ ϵ CM [I) and either ϕ or ψ is twice continuously
differentiable on I.