Functional equation; Linearly dependent functions; Mean value theorem
Aequationes Mathematicae, Vol. 92, no. 5 (2018), s. 935-947
The aim of this paper is to describe the solution (f, g) of the equation [f(x)-f(y)]g′(αx+(1-α)y)=[g(x)-g(y)]f′(αx+(1-α)y),x,y∈I,where I⊂ R is an open interval, f, g: I→ R are differentiable, α is a fixed number from (0, 1).