On a General Conditional Cauchy Functional Equation - Elham Mohammadi; Abbas Najati; Yavar Khedmati Yengejeh (Sahand Communications in Mathematical Analysis)
Let $(G,+)$ be an abelian group and $Y$  a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in G,\] for functions $f:G\to Y$, where  $a,b\in \Bbb{F}$ are fixed constants. The general solution and stability of this functional equation are described.