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 Lp-norm is given.
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References
J. Aczel: ‘Lectures on Functional Equations and their Applications’, Academic Press, New York-London, 1966.
M. Kuczma: ‘Functional Equations in a Single Variable’, Monografic Mat. 46, Polish Scientific Publishers (PWN ), Warszawa, 1968.
M. Kuczma: ‘An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality’, Polish Scientific Publishers (PWN), Silesian University, Warszawa-KrakowKatowice, 1985.
J. Matkowski: ‘Cauchy functional equation on a restricted domain and commuting functions’, pages 101–106 In: Iteration Theory and its Functional Equations, Proc., Schloss Hofen 1984, Springer Verlag, 1985.
J. Matkowski: ‘On a characterization of LP-norm’, Ann. Polon. Math. 50 (1989), 137–144.
J. Matkow ski: ‘The converse of the Minkowski’s inequality theorem and its generalization’, Proc. Amer. Math. Soc. 109 (1990), 663–675.
J. Matkowski and M. Sablik.
W. Wnuk: ‘Orlicz spaces cannot be normed analogously to LP-spaces’, Indagationes Math. 46 (1984), 357–359.
A. C. Zaanen: ‘Some remarks about the definition of an Orlicz space’, Lecture Notes 945 (1982), 263–268.
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© 2003 Springer Science+Business Media Dordrecht
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Krassowska, D., Matkowski, J. (2003). A Pair of Functional Inequalities of Iterative Type Related to a Cauchy Functional Equation. In: Rassias, T.M. (eds) Functional Equations, Inequalities and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0225-6_6
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DOI: https://doi.org/10.1007/978-94-017-0225-6_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6406-6
Online ISBN: 978-94-017-0225-6
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