An extension theorem for a Matkowski-Sutô problem

Zoltán Daróczy, Gabriella Hajdu, and Che Tat Ng. "An extension theorem for a Matkowski-Sutô problem." Colloquium Mathematicae 95.2 (2003): 153-161. <http://eudml.org/doc/284995>.

@article{ZoltánDaróczy2003,
abstract = {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.},
author = {Zoltán Daróczy, Gabriella Hajdu, Che Tat Ng},
journal = {Colloquium Mathematicae},
keywords = {functional equations; mean values; quasilinear; quasiarithmetic; extension of solutions; general continuous strictly monotonic solution},
language = {eng},
number = {2},
pages = {153-161},
title = {An extension theorem for a Matkowski-Sutô problem},
url = {http://eudml.org/doc/284995},
volume = {95},
year = {2003},
}

TY - JOUR
AU - Zoltán Daróczy
AU - Gabriella Hajdu
AU - Che Tat Ng
TI - An extension theorem for a Matkowski-Sutô problem
JO - Colloquium Mathematicae
PY - 2003
VL - 95
IS - 2
SP - 153
EP - 161
AB - 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.
LA - eng
KW - functional equations; mean values; quasilinear; quasiarithmetic; extension of solutions; general continuous strictly monotonic solution
UR - http://eudml.org/doc/284995
ER -