Extensions in Time Scales Integral Inequalities of Jensen's Type via Fink's Identity

In this paper, using Fink's identity and Green's function, we obtain several extensions of Jensen's inequality, Jensen-Steffensen inequality, and the converse of Jensen's inequality for diamond integrals. Functions involved in these extensions are n-convex functions, n ϵ ℤ+. Some bounds for related identities are also part of the discussion. An improved Hölder's inequality is obtained as an application of improved Jensen's inequality. © 2023 Mathematical Institute Slovak Academy of Sciences.