2024/105/1-2 (15)
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DOI: 10.5486/PMD.2024.9878
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pp. 233-257
Characterizing locally polynomial functions on convex subsets of linear spaces
Authors:
Chisom Prince Okeke 
and Maciej Sablik
Abstract:
We introduce the notion of locally polynomial functions, satisfying a conditional Fréchet equation on convex subsets of linear space. We prove that locally polynomial functions are solutions to some rather general functional equations. Using Roman Ger's result, we infer that locally they are the restrictions of polynomial functions defined on the whole space.
Keywords: functional equations, polynomial functions, absolutely convex sets, algebraic interior, Fréchet operator, monomial functions, continuity of monomial functions
Mathematics Subject Classification: 39B52, 39A70, 39-04