On a Functional Equation Containing Weighted Arithmetic Means

  • Adrienn Varga
  • Csaba Vincze
Part of the International Series of Numerical Mathematics book series (ISNM, volume 157)


In this paper we solve the functional equation
$$ \sum\limits_{i = 1}^n {a_i f(\alpha _i x + (1 - \alpha _i )y) = 0} $$
which holds for all x, yI, where I ⊂ ℝ is a non-void open interval, f : I → ℝ is an unknown function and the weights α i ∈ (0, 1) are arbitrarily fixed (i = 1, . . ., n). It will be proved that all solutions are generalized polynomials of degree at most n − 2. Furthermore we give a sufficient condition for the existence of nontrivial solutions.


Functional equation p-Wright and Jensen affine functions 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Adrienn Varga
    • 1
  • Csaba Vincze
    • 1
  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary

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