Displaying similar documents to “A new analogue of Gauss' functional equation.”

A Gauss type functional equation.

Toader, Silvia, Rassias, Themistocles M., Toader, Gheorghe (2001)

International Journal of Mathematics and Mathematical Sciences

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A functional equation related to an equality of means problem

Janusz Matkowski (2011)

Colloquium Mathematicae

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The functional equation (F(x)-F(y))/(x-y) = (G(x)+G(y))(H(x)+H(y)) where F,G,H are unknown functions is considered. Some motivations, coming from the equality problem for means, are presented.

Some mean value theorems as consequences of the Darboux property

Dan Ştefan Marinescu, Mihai Monea (2017)

Mathematica Bohemica

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The aim of the paper is to present some mean value theorems obtained as consequences of the intermediate value property. First, we will prove that any nonextremum value of a Darboux function can be represented as an arithmetic, geometric or harmonic mean of some different values of this function. Then, we will present some extensions of the Cauchy or Lagrange Theorem in classical or integral form. Also, we include similar results involving divided differences. The paper was motivated...

An extension theorem for a Matkowski-Sutô problem

Zoltán Daróczy, Gabriella Hajdu, Che Tat Ng (2003)

Colloquium Mathematicae

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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.