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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  ∈   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.

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