Refinements of jensen’s and mcshane’s inequalities with applications

In this article, we consider the generalized forms of the Jensen’s inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen’s and McShane’s inequalities connected to certain functions from the linear space, generalize the Jessen’s and McShane’s inequalities pertaining n certain functions. As applications, we provide some improvements for the generalized means, Hölder and generalized Beck’s inequalities. © 2020 the Author(s), licensee AIMS Press.