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

  • Dorota Krassowska
  • Janusz Matkowski

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 Lp-norm-like functional subhomogeneity characterization of Lp-norm 

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Dorota Krassowska
    • 1
  • Janusz Matkowski
    • 1
  1. 1.Institute of MathematicsUniversity of Zielona GóraZielona GóraPoland

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