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Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings

Abstract This paper is motivated by the recent progress on the Hermite–Hadamard inequality for convex functions defined on the bounded closed interval, obtained by Z. Pavić [Z. Pavić, Improvements of the Hermite–Hadamard inequality, J. Inequal. Appl. 2015 2015, Article ID 222]. As a generalization, we obtained a new refinement of the Hermite–Hadamard inequality for co-ordinated convex functions defined on the rectangle.