The Hermite-Hadamard inequality for r-convex functionsReport as inadecuate

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Journal of Inequalities and Applications

, 2012:215

First Online: 02 October 2012Received: 14 March 2012Accepted: 13 September 2012


In this paper, we establish the Hermite-Hadamard inequality for r-convex functions. We prove that r-convexity implies s-convexity 0 ≤ r ≤ s Open image in new window. As a result, we obtain a refinement of the Hermite-Hadamard inequality for an r-convex function 0 ≤ r ≤ 1 Open image in new window. We also investigate the Hermite-Hadamard inequality for the product of an r-convex function f and an s-convex function g.

MSC: 26D15, 26D10.

KeywordsHermite-Hadamard inequality integral inequality  Download fulltext PDF

Author: Gholamreza Zabandan - Abasalt Bodaghi - Adem Kılıçman


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