Abstract We study a type of calculus for proving inequalities between subgraph densities that is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erdös-Simonovits and Sidorenko for various families of graphs. In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.
Li et al. (Sun,) studied this question.