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arXiv · 1307.0653

General and alien solutions of a functional equation and of a functional inequality

Włodzimierz Fechner·Eszter Gselmann
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Abstract

The purpose of the present paper is to solve (under some assumption on the domain) the equation $$ g(x+y)-g(x)-g(y)=xf(y)+yf(x). $$ After determining the general solutions, we will investigate the so--called alien solutions. %More precisely, we will examine the cases when the above equation implies that %$g(x+y)=g(x)+g(y)$ and $xf(y)+yf(x)=0$. %Concerning this, necessary and sufficient conditions will be provided. Finally, we will discuss the real solutions of the following related functional inequality: $$ g(x+y)-g(x)-g(y)\geq xf(y)+yf(x). $$

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Włodzimierz Fechner, Eszter Gselmann. 2013-07-02. General and alien solutions of a functional equation and of a functional inequality. https://arxiv.org/abs/1307.0653

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