Aequationes mathematicae

, Volume 75, Issue 1–2, pp 130–148 | Cite as

Some extension theorems for n-Jensen functions and functional equations characterizing generalized polynomials



The object of this paper is to investigate possibilities of extending the solution F : CW of certain functional equations to V and of n-Jensen functions f : C n W to V n , where C is a \({\mathbb{Q}}\) -convex subset of V and V, W are \({\mathbb{Q}}\) -vector spaces. Solutions of the considered functional equations defined on V and n-Jensen functions defined on V n have been utilized in recent papers (e.g. [2], [4]) in order to characterize generalized polynomials P : VW of degree  ≤ n. Therefore these extension theorems may present a point of view for defining generalized polynomials on a \({\mathbb{Q}}\) -convex subset of a \({\mathbb{Q}}\) -vector space.

Even more generally, we consider certain functional equations for functions f : CW, where C is an L-convex subset of an L-vector space V and L is an arbitrary subfield of \({\mathbb{R}}\) , possibly different from \({\mathbb{Q}}\) .

Mathematics Subject Classification (2000).

39B52 39A70 68U05 41A10 


Generalized polynomials functional equations multi-Jensen functions extension 


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Copyright information

© Birkhäuser Verlag AG 2008

Authors and Affiliations

  1. 1.Institut für MathematikKarl-Franzens Universität GrazGrazAustria

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