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 Hermite-Hadamard type inequalities for geometric-arithmetically $\boldsymbol{s}$-convex functions Commun. Korean Math. Soc. 2014 Vol. 29, No. 1, 51-63 https://doi.org/10.4134/CKMS.2014.29.1.51Printed January 31, 2014 J\"u Hua, Bo-Yan Xi, and Feng Qi Inner Mongolia Normal University, Inner Mongolia University for Nationalities, Tianjin Polytechnic University Abstract : In the paper, several properties of geometric-arithmetically $s$-convex functions are provided, an integral identity in which the integrands are products of a function and a derivative is found, and then some inequalities of Hermite-Hadamard type for integrals whose integrands are products of a derivative and a function whose derivative is of the geometric-arithmetic $s$-convexity are established. Keywords : property, identity, Hermite-Hadamard integral inequality, geometric-arithmetically $s$-convex function MSC numbers : Primary 26D15; Secondary 26A51, 41A55 Downloads: Full-text PDF

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