The inhomogeneous general linear functional equation

Prager, Wolfgang; Schwaiger, Jens

doi:10.1007/s00010-014-0295-1

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2019

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“…The main novelty of the proof is a general version of a result Radó and Baker [13] on the existence and uniqueness of extension of the solution of the classical Pexider equation (see Theorem 1.6 below). We refer to [9, Chapter 13.10] and [8,11,12] for the classical theory of general linear equations and references therein.…”

Section: Introductionmentioning

confidence: 99%

The general linear equation on open connected sets

Leonetti

Schwaiger

2019

Acta Math. Hungar.

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Fix non-zero reals α 1 , . . . , α n with n ≥ 2 and let K be a non-empty open connected set in a topological vector space such that i≤n α i K ⊆ K (which holds, in particular, if K is an open convex cone and α 1 , . . . , α n > 0). Let also Y be a vector space over F := Q(α 1 , . . . , α n ). We show, among others, that a function f : K → Y satisfies the general linear equationThe main tool of the proof is a general version of a result Radó and Baker on the existence and uniqueness of extension of the solution on the classical Pexider equation.

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