Monotonic solutions of a composite functional equation

Chao first considered the composite functional equation aligned f(x + 2f(y)) = f(x) + y + f(y) (x, y ∈ R), aligned where f: R → R . This equation was studied by several mathematicians. In this paper, we study the monotonic solutions of the composite functional equation aligned f(xyf(y)) = f(x) y f(y) (x, y ∈ R), aligned where f: R → R . This equation is similar to Chao’s equation.