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On Hermite-Hadamard type inequalities for \(s\)-convex functions on the coordinates via Riemann-Liouville fractional integrals. (English) Zbl 1437.26026

Summary: We obtain some Hermite-Hadamard type inequalities for \(s\)-convex functions on the coordinates via Riemann-Liouville integrals. Some integral inequalities with the right-hand side of the fractional Hermite-Hadamard type inequality are also established.

MSC:

26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals
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[1] Farid, G.; Abramovich, S.; Pečarić, J., More about Hermite-Hadamard inequalities, Cauchy’s means, and superquadracity, Journal of Inequalities and Applications, 2010 (2010) · Zbl 1205.26028
[2] Bessenyei, M.; Páles, Z., Hadamard-type inequalities for generalized convex functions, Mathematical Inequalities & Applications, 6, 3, 379-392 (2003) · Zbl 1043.26009
[3] Dragomir, S. S.; Fitzpatrick, S., The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Mathematica, 32, 4, 687-696 (1999) · Zbl 0952.26014
[4] Dragomir, S. S., On the Hadamard’s inequlality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 5, 4, 775-788 (2001) · Zbl 1002.26017
[5] El Farissi, A., Simple proof and refinement of Hermite-Hadamard inequality, Journal of Mathematical Inequalities, 4, 3, 365-369 (2010) · Zbl 1197.26017
[6] Gao, X., A note on the Hermite-Hadamard inequality, Journal of Mathematical Inequalities, 4, 4, 587-591 (2010) · Zbl 1208.26033
[7] Sarikaya, M. Z.; Set, E.; Yildirim, H., On some Hadamard-type inequalities for h-convex functions, Journal of Mathematical Inequalities, 2, 3, 335-341 (2008) · Zbl 1166.26302
[8] Hudzik, H.; Maligranda, L., Some remarks on s-convex functions, Aequationes Mathematicae, 48, 1, 100-111 (1994) · Zbl 0823.26004
[9] Alomari, M.; Darus, M., The Hadamard’s inequality for s-convex function of 2-variables on the co-ordinates, International Journal of Mathematical Analysis, 2, 13, 629-638 (2008) · Zbl 1178.26017
[10] Alomari, M.; Darus, M., Hadamard-type inequalities for s-convex functions, International Mathematical Forum, 3, 40, 1965-1975 (2008) · Zbl 1163.26325
[11] Sarikaya, M. Z.; Set, E.; Yaldiz, H.; Başak, N., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57, 9-10, 2403-2407 (2013) · Zbl 1286.26018
[12] Sarıkaya, M. Z., On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, 25, 2, 134-147 (2014) · Zbl 1284.26008
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