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arXiv · 2501.08949

On the Kurepa and inhomogeneous Cauchy functional equations

Rashid Aliev·Vugar Ismailov
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Abstract

It follows from de Bruijn's results that if a continuous or $k$-th order continuously differentiable function $F(x,y)$ is a solution of the Kurepa functional equation, then it can be expressed as $F(x,y)=f(x+y)-f(x)-f(y)$ with the continuous $f$ or the $k$-th order continuously differentiable $f$, respectively. These two facts strengthen the corresponding results of Kurepa and Erd\"{o}s. In this paper, we provide new and constructive proofs for these facts. In addition to practically useful recipes given here for construction of $f$, we also estimate its modulus of continuity.

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Rashid Aliev, Vugar Ismailov. 2025-01-15. On the Kurepa and inhomogeneous Cauchy functional equations. https://arxiv.org/abs/2501.08949

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