Some Generalizations of Jensen's Inequality

  • Slavko Simic Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia
  • Bandar Almohsen College of Science, Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
Keywords: Jensen's inequality, Jensen-Mercer inequality, twice differentiable functions, convex functions


In this article, we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They represent a refinement of these inequalities in the case of convex/concave functions with numerous applications in Theory of Means and Probability and Statistics.

How to Cite
Slavko Simic, Bandar Almohsen. Some Generalizations of Jensen’s Inequality. Contemporary Mathematics [Internet]. 2020Dec.26 [cited 2021Jan.22];2(1). Available from: