engleski

Improved Jensen-type inequalities via linear interpolation and applications

In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence, we obtain improvements of some recently established Young-type inequalities. Finally, our method is also applied to matrix case. In such a way we obtain improvements of some important matrix inequalities known from the literature.

convex function ; Jensen inequality ; Young inequality ; Kantorovich constant ; Specht ratio ; arithmetic mean ; geometric mean ; Heinz mean

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