## On the solutions of the functional equation $$f(xf(y)^ l + yf(x)^ k) = tf(x)f(y)$$.(English)Zbl 0741.39008

Using some elementary but elegant methods the author proves that the only continuous solutions $$f:\mathbb{R}\to\mathbb{R}$$ of the equation in title are constants $$f=0$$ and $$f=1/t$$. The same is true if $$f:X\to\mathbb{R}$$ where $$X$$ is a real linear space and $$f$$ is continuous along rays.

### MSC:

 39B22 Functional equations for real functions 39B52 Functional equations for functions with more general domains and/or ranges

### Keywords:

continuous solutions; linear space