A refinement of the integral form of Jensen’s inequality
Department of Mathematics, University of Pannonia, Egyetem u. 10, Veszprém, 8200, Hungary
Journal of Inequalities and Applications 2012, 2012:178 doi:10.1186/1029-242X-2012-178Published: 16 August 2012
There are a lot of refinements of the discrete Jensen’s inequality, and this problem has been studied by many authors. It is also a natural problem to give analogous results for the classical Jensen’s inequality. In spite of this, few papers have been published dealing with this problem. The purpose of this paper is to give some refinements of the classical Jensen’s inequality. The results give a new approach of this topic. Moreover, new discrete inequalities can be derived, and the integral analogous of discrete inequalities can be obtained. We also have new refinements of the left-hand side of the Hermite-Hadamard inequality.
MSC: 26D07, 26A51.