Abstract
We discuss the following problem: Under which assumptions on h: ℝ+ → ℝ has the difference equation f(x+1) - f(x) = h(x), X ∈ ℝ, exactly one convex solution, normalized by f(1) = 0 ? The problem is completely solved in the case inf \(\left\{ {\text{h(n + 1)}\,\text{ - }\,\text{h(n)}|\text{n} \in \mathbb{N}} \right\} = 0\).
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References
W. Krull, Bemerkungen zur Differenzengleichung g(x+1) — g (x) = ф (x). Math. Nachr. 1 (1948), 365–376.
M. Kuczma, Functional equations in a single variable. Polish Scientific Publishers, Warszawa, 1968.
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© 1987 Birkhäuser Verlag Basel
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Kairies, HH. (1987). Bemerkungen zu Einem Existenz- und Eindeutigkeitsproblem von W. Walter aus dem Gebiet der Differenzengleichungen. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_24
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DOI: https://doi.org/10.1007/978-3-0348-7192-1_24
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7194-5
Online ISBN: 978-3-0348-7192-1
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