A Pair of Functional Inequalities of Iterative Type Related to a Cauchy Functional Equation

Dorota Krassowska () and Janusz Matkowski ()
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Dorota Krassowska: University of Zielona Góra, Institute of Mathematics
Janusz Matkowski: University of Zielona Góra, Institute of Mathematics

Chapter Chapter 6 in Functional Equations, Inequalities and Applications, 2003, pp 73-89 from Springer

Abstract: Abstract It is shown that, under some general algebraic conditions on fixed real numbers a, b, α, β, every continuous at a point solution f of the system of functional inequalities f(x + a) ≤ f(x) + α, f(x + b) ≤ f(x) + β (x ∈ ℝ) must be a polynomial of order 1. Analogous results for three remaining counterparts of this simultaneous system are presented. An application to characterization of L p -norm is given.

Keywords: functional inequality; functional equation; Kronecker’s theorem; L p -norm-like functional; subhomogeneity; characterization of L p -norm (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0225-6_6

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DOI: 10.1007/978-94-017-0225-6_6

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