New refinements of the jensen-mercer inequality associated to positive n-tuples

In this manuscript, we propose new refinements for the Jensen-Mercer as well as variant of the Jensen-Mercer inequalities associated to certain positive tuples. We give some related integral version and present applications for different means. At the end, further generalizations are given which are associated to m finite sequences.2. © 2020, Republic of Armenia National Academy of Sciences. All rights reserved.