Let I be an interval, 0 < λ < 1 be a fixed constant and A(x,y) = λx + (1-λ)y, x,y ∈ I, be the weighted arithmetic mean on I. A pair of strict means M and N is complementary with respect to A if A(M(x,y),N(x,y)) = A(x,y) for all x, y ∈ I. For such a pair we give results on the functional equation f(M(x,y)) = f(N(x,y)). The equation is motivated by and applied to the Matkowski-Sutô problem on complementary weighted quasi-arithmetic means M and N.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-1,
author = {Zolt\'an Dar\'oczy and Gabriella Hajdu and Che Tat Ng},
title = {An extension theorem for a Matkowski-Sut\^o problem},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {153-161},
zbl = {1031.39016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-1}
}
Zoltán Daróczy; Gabriella Hajdu; Che Tat Ng. An extension theorem for a Matkowski-Sutô problem. Colloquium Mathematicae, Tome 96 (2003) pp. 153-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-1/