Geodesic
An extension theorem for a Matkowski–Sutô problem
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
Colloquium Mathematicum, Tome 95 (2003) no. 2, pp. 153-161 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 
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     title = {An extension theorem 
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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

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