Complete monotonicity of solutions of the Abel equation $F(e^x)=F(x)+1$

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چکیده

We investigate the functions $F:\mathbb R\to \mathbb R$ which are $C^\infty $ solutions of Abel functional equation $F(e^x)= F(x)+1$. In particular, we determine asymptotic behaviour derivatives and show that no solution can have $F’$ compl

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منابع مشابه

On Monotonic Solutions of an Integral Equation of Abel Type

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ژورنال

عنوان ژورنال: Bulletin of the Polish Academy of Sciences. Mathematics

سال: 2023

ISSN: ['0239-7269', '1732-8985']

DOI: https://doi.org/10.4064/ba230411-18-6