On a Problem of Alsina Again

We give some new results concerning the functional equation fŽx y. fŽfŽx. fŽy.. f fŽx fŽy.. fŽfŽx. y. , proposed by C. Alsina in 1986. We also investigate a related equation zfŽx y. fŽfŽx. fŽy.. f fŽx zfŽy.. fŽzfŽx. y. and we solve it in the class of decreasing involutions ofŽ0, .onto itself.