Geodesic
An extension theorem for a Matkowski–Sutô problem
Zoltán Daróczy1 ; Gabriella Hajdu1 ; Che Tat Ng2
1 Institute of Mathematics and Informatics Lajos Kossuth University H-4010 Debrecen, Pf. 12 Hungary
2 Department of Pure Mathematics University of Waterloo Waterloo, ON, Canada N2L 3G1
Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 153-161.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $I$ be an interval, $0\lambda 1$ be a fixed constant and $A(x,y)=\lambda x+(1-\lambda ) y,\, x,y \in I,$ 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 $x, y \in I.$ 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 $N$.
DOI : 10.4064/cm95-2-1
Keywords: interval lambda fixed constant lambda lambda weighted arithmetic mean pair strict means complementary respect y pair results functional equation y y equation motivated applied matkowski sut problem complementary weighted quasi arithmetic means

Zoltán Daróczy 1 ; Gabriella Hajdu 1 ; Che Tat Ng 2

1 Institute of Mathematics and Informatics Lajos Kossuth University H-4010 Debrecen, Pf. 12 Hungary
2 Department of Pure Mathematics University of Waterloo Waterloo, ON, Canada N2L 3G1 
@article{10_4064_cm95_2_1,
     author = {Zolt\'an Dar\'oczy and Gabriella Hajdu and Che Tat Ng},
     title = {An extension theorem 
  for a {Matkowski{\textendash}Sut\^o} problem},
     journal = {Colloquium Mathematicum},
     pages = {153--161},
     publisher = {mathdoc},
     volume = {95},
     number = {2},
     year = {2003},
     doi = {10.4064/cm95-2-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-1/}
}
TY  - JOUR
AU  - Zoltán Daróczy
AU  - Gabriella Hajdu
AU  - Che Tat Ng
TI  - An extension theorem 
  for a Matkowski–Sutô problem
JO  - Colloquium Mathematicum
PY  - 2003
SP  - 153
EP  - 161
VL  - 95
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-1/
DO  - 10.4064/cm95-2-1
LA  - en
ID  - 10_4064_cm95_2_1
ER  - 
%0 Journal Article
%A Zoltán Daróczy
%A Gabriella Hajdu
%A Che Tat Ng
%T An extension theorem 
  for a Matkowski–Sutô problem
%J Colloquium Mathematicum
%D 2003
%P 153-161
%V 95
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-1/
%R 10.4064/cm95-2-1
%G en
%F 10_4064_cm95_2_1
Zoltán Daróczy; Gabriella Hajdu; Che Tat Ng. An extension theorem 
  for a Matkowski–Sutô problem. Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 153-161. doi : 10.4064/cm95-2-1. http://geodesic.mathdoc.fr/articles/10.4064/cm95-2-1/

Cité par Sources :