On the refinement of Jensen’s inequality

The main purpose of this work is to present the extension of the recent results given by Dragomir [S.S. Dragomir, A new refinement of Jensen’s inequality in linear spaces with applications, Math. Comput. Model. 52 (2010) 1497–1505], where new refinement of Jensen’s inequality is presented and given applications in the information theory. Our work improves the basic result of Dragomir through a stronger refinement of Jensen’s inequality which is then applied to the Information Theory and obtained stronger lower bounds for the mean f-deviation and f-divergences.