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

• Autores: Jens Schwaiger, Wolfgang Prager
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 75, Nº. 1-2, 2008, págs. 130-148
• Idioma: inglés
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• Resumen

  • The object of this paper is to investigate possibilities of extending the solution F : C ? W of certain functional equations to V and of n-Jensen functions f : C n ? W to V n , where C is a -convex subset of V and V, W are -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 : V ?W of degree = n. Therefore these extension theorems may present a point of view for defining generalized polynomials on a -convex subset of a -vector space. Even more generally, we consider certain functional equations for functions f : C ?W, where C is an L-convex subset of an L-vector space V and L is an arbitrary subfield of , possibly different from.