A generalized Jensen's inequality for bounded analytic functions (Q1892735)

In this paper the author analizes the various recent generalisations of Jensen's inequality for bounded analytic functions. Here he gives a general theorem that can be viewed as a strengthening of the classical Jensen's inequality. Some consequences of the theorem are also discussed and it is shown that the theorem also improves upon an earlier result of the author [Numer. Math. 49, 221-225 (1986; Zbl 0597.30006)]. The inequality established is shown to be the best possible in certain sense.