On Jessen's inequality for convex functions. II (Q1086373)

A short proof of the Jessen's inequality, some complementary inequalities and applications were given by the authors in the first paper with this title [J. Math. Anal. Appl. 110, 536--552 (1985; Zbl 0591.26009)]. Now they give some refinements and improvements of the Jessen's inequality, together with applications to extensions of Knopp's and Hadamard's inequality for convex functions. They also consider generalizations of a number of classical inequalities involving mean values of various kinds, as well as Hölder type inequalities. Finally, the authors extend some inequalities for real isotonic functionals to complex linear functionals given by \(\bar A(f)=A(\text{Re}\, f)+iA(\text{Im}\, f)\).