A Refinement of Jensen's Inequality via Superquadratic Functions
Asare-Tuah Anton *
Department of Mathematics, University of Ghana, Legon, Ghana.
Prempeh Edward
Department of Mathematics, Kwame Nkrumah University of Science and Technology (KNUST), Ghana.
*Author to whom correspondence should be addressed.
Abstract
We establish the inequality
where 
is superquadratic and
prove a more general inequality where 1/2n and 2n -1/2n are replaced by a/2n and b/2n respectively, with a+b=2n ,n ∈ N, the latter is extended to the case where
a+b ≠ 2n , n ∈ N.
Keywords: Convex function, Midconvex function, Superquadratic function, Jensen's inequality and Rened Jensen's inequality