Improved Jensen-type inequalities via linear interpolation and applications
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 …