×

Some new generalized integral inequalities for GA-\(s\)-convex functions via Hadamard fractional integrals. (English) Zbl 1360.26021

Summary: We prove new generalization of Hadamard, Ostrowski, and Simpson inequalities in the framework of GA-\(s\)-convex functions and Hadamard fractional integral.

MSC:

26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals
26A51 Convexity of real functions in one variable, generalizations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Breckner, W. W., Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Publications de l’Institut Mathématique, 23, 13-20 (1978) · Zbl 0416.46029
[2] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Elsevier · Zbl 1092.45003
[3] Alomari, M.; Darus, M.; Dragomir, S. S.; Cerone, P., Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Applied Mathematics Letters, 23, 9, 1071-1076 (2010) · Zbl 1197.26021 · doi:10.1016/j.aml.2010.04.038
[4] Avci, M.; Kavurmaci, H.; Özdemir, M. E., New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications, Applied Mathematics and Computation, 217, 12, 5171-5176 (2011) · Zbl 1209.26022 · doi:10.1016/j.amc.2010.11.047
[5] Dragomir, S. S.; Fitzpatrik, S., The Hadamard’s inequality for \(s\)-convex functions in the second sense, Demonstratio Mathematica, 32, 4, 687-696 (1999) · Zbl 0952.26014
[6] İşcan, İ., New estimates on generalization of some integral inequalities for s-convex functions and their applications, International Journal of Pure and Applied Mathematics, 86, 4, 727-746 (2013) · doi:10.12732/ijpam.v86i4.11
[7] Park, J., Generalization of some Simpson-like type inequalities via differentiable \(s\)-convex mappings in the second sense, International Journal of Mathematics and Mathematical Sciences, 2011 (2011) · Zbl 1221.26033 · doi:10.1155/2011/493531
[8] Set, E., New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Computers & Mathematics with Applications, 63, 7, 1147-1154 (2012) · Zbl 1247.26038 · doi:10.1016/j.camwa.2011.12.023
[9] Sarıkaya, M. Z.; Set, E.; Özdemir, M. E., On new inequalities of Simpson’s type for s-convex functions, Computers & Mathematics with Applications, 60, 8, 2191-2199 (2010) · Zbl 1205.65132 · doi:10.1016/j.camwa.2010.07.033
[10] Sarıkaya, M. Z.; Set, E.; Yaldız, 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 · doi:10.1016/j.mcm.2011.12.048
[11] Niculescu, C. P., Convexity according to the geometric mean, Mathematical Inequalities & Applications, 3, 2, 155-167 (2000) · Zbl 0952.26006 · doi:10.7153/mia-03-19
[12] Niculescu, C. P., Convexity according to means, Mathematical Inequalities & Applications, 6, 4, 571-579 (2003) · Zbl 1047.26010 · doi:10.7153/mia-06-53
[13] Shuang, Y.; Yin, H.-P.; Qi, F., Hermite-Hadamard type integral inequalities for geometric-arithmetically \(s\)-convex functions, Analysis, 33, 2, 197-208 (2013) · Zbl 1272.26024 · doi:10.1524/anly.2013.1192
[14] Hua, J.; Xi, B.-Y.; Qi, F., Hermite-Hadamard type inequalities for geometric-arithmetically s-convex functions, Communications of the Korean Mathematical Society, 29, 1, 51-63 (2014) · Zbl 1292.26048
[15] İscan, İ., Hermite-Hadamard type inequalities for GA-s-convex functions, Le Matematiche, 69, 2, 129-146 (2014) · Zbl 1320.26025 · doi:10.4418/2014.69.2.12
[16] Kunt, M.; İşcan, İ., On new inequalities of Hermite-Hadamard-Fejer type for GA-s-convex functions via fractional integrals, Konuralp Jurnal of Mathematics, 4, 1, 130-139 (2016) · Zbl 1355.26011
[17] Maden, S.; Turhan, S.; İşcan, İ., New Hermite-Hadamard-Fejer type inequalities for GA-convex functions, Proceedings of the AIP Conference · Zbl 1092.45003 · doi:10.1063/1.4945869
[18] Zhang, X.-M.; Chu, Y.-M.; Zhang, X.-H., The Hermite-Hadamard type inequality of GA-convex functions and its application, Journal of Inequalities and Applications, 2010 (2010) · Zbl 1187.26012 · doi:10.1155/2010/507560
[19] Zhang, T.-Y.; Ji, A.-P.; Qi, F., Some inequalities of Hermite-HADamard type for GA-convex functions with applications to means, Le Matematiche, 68, 1, 229-239 (2013) · Zbl 1281.26024
[20] Wang, J.; Deng, J.; Fečkan, M., Exploring s-e-condition and applications to some Ostrowski type inequalities via Hadamard fractional integrals, Mathematica Slovaca, 64, 6, 1381-1396 (2014) · Zbl 1349.26021 · doi:10.2478/s12175-014-0281-z
[21] İşcan, İ., New general integral inequalities for quasi-geometrically convex functions via fractional integrals, Journal of Inequalities and Applications, 2013, article 491 (2013) · Zbl 1297.26008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.