Some Hadamard and Simpson type inequalities via s-convexity and their applications

[1] M. Alomari, M. Darus, S. S. Dragomir, New inequalities of Simpson’s type for s-convex functions with applications, RGMIA Res. Rep. Coll., Article 9, vol. 12, no.4, 2009.Search in Google Scholar

[2] G. A. Anastassiou, Taylor Widder representation formulae and Ostrowski, Grüss, integral means and Csiszar type inequalities, Comp&Math Appl., vol. 54, 2007, 9–23.10.1016/j.camwa.2006.09.010Search in Google Scholar

[3] M. Bessenyei, Z. Páles, Characterization of convexity via Hadamard’s inequality, Math. Inequal. Appl., vol. 9, 2006, 53–62.10.7153/mia-09-06Search in Google Scholar

[4] S. S. Dragomir, R. P. Agarwal, P. Cerone, On Simpson’s inequality and applications, Journal of Ineq. and Appl., vol. 5, 2000, 533–579.10.1155/S102558340000031XSearch in Google Scholar

[5] S. S. Dragomir, C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA monographs, Victoria University, 2000.Search in Google Scholar

[6] J. Hadamard, Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl., vol. 58, 1893, 171–215.Search in Google Scholar

[7] H. Hudzik, L. Maligranda, Some remarks on s -convex functions, Aequationes Math., vol. 48, 1994, 100–111.10.1007/BF01837981Search in Google Scholar

[8] D. S. Mitrinović, I. B. Lacković, Hermite and convexity, Aequationes Math., vol. 28, 1985, 229–232.10.1007/BF02189414Search in Google Scholar

[9] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, 1993.Search in Google Scholar

[10] C. P. Niculescu, L. Persson, Convex Functions and their Applications, A Contemporary Approach, in: CMS Books in Mathematics, 23, Springer-Verlag, New York, 2006.10.1007/0-387-31077-0Search in Google Scholar

[11] M. Z. Sarikaya, E. Set, M. E. Özdemir, On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll., Article 2, vol. 13, no. 2, 2010.Search in Google Scholar

[12] M. Z. Sarikaya, E. Set, M. E. Özdemir, On new inequalities of Simpson’s type for s-convex functions, Comp&Math Appl, vol. 60, 2010, 2191–2199.10.1016/j.camwa.2010.07.033Search in Google Scholar

[13] S. Wu, L. Debnath, Inequalities for convex sequences and their applications, Comp&Math Appl., vol. 54, 2007, 525–534.10.1016/j.camwa.2007.02.005Search in Google Scholar

[14] B. Y. Xi, F. Qi, Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means, Journal of Function Spaces and Appl., Article ID 980438, vol. 2012, doi: 10.1155/2012/980438.10.1155/2012/980438Search in Google Scholar