A generalization of Mercer’s result on convex functions

In this paper we generalize a result of Mercer [A.McD. Mercer, A variant of Jensen’s inequality, J. Inequal. Pure & Appl. Math. 4 (4) (2003) Article 73. Online:http://jipam.vu.edu.au/article.php?sid=314] on convex functions. A relationship between this result and majorization ordering is pointed out. An extension of Mercer’s result to pairs of similarly separable m-tuples is given. In addition, applications are discussed for nonincreasing in mean tuples, star-shaped tuples and convex tuples.