Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized \(s\)-convex in the second sense. (English) Zbl 1462.26023
Summary: In this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized \(s\)-convex in the second sense.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A33 | Fractional derivatives and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
Keywords:
generalized Hermite-Hadamard inequality; generalized Hölder inequality; generalized convex functionsReferences:
| [1] | Budak, H.; Sarikaya, M. Z.; Yildirim, H., New inequalities for local fractional integrals, Iranian Journal of Science and Technology (Sciences) · Zbl 1390.26036 |
| [2] | Chen, G-S., Generalizations of Hölder’s and some related integral inequalities on fractal space, Journal of Function Spaces and Applications Volume (2013) · Zbl 1275.26014 |
| [3] | Kılıçman, A.; Saleh, W., Notions of generalized s-convex functions on fractal sets, Journal of Inequalities and Applications, 312 (2015) · Zbl 1336.26010 · doi:10.1186/s13660-015-0826-x |
| [4] | Mo, H.; Sui, X.; Yu, D., Generalized convex functions on fractal sets and two related inequalities, Abstract and Applied Analysis (2014) · Zbl 1474.26128 |
| [5] | Mo, H., Generalized Hermite-Hadamard inequalities involving local fractional integrals, arXiv:1410.1062 [math.AP] |
| [6] | Mo, H.; Sui, X., Generalized s-convex function on fractal sets, arXiv:1405.0652v2 [math.AP] |
| [7] | Mo, H.; Sui, X., Hermite-Hadamard type inequalities for generalized s-convex functions on real linear fractal set \(R^{\alpha} \alpha(0 < \alpha < 1)\), arXiv:1506.07391v1 [math.CA] · Zbl 1407.26025 |
| [8] | Ostrowski, A. M., Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv., 10, 226-227 (1938) · JFM 64.0209.01 |
| [9] | Saleh, W.; Kılıçman, A., On generalized s-convex functions on fractal set, JP Journal of Geometry and Topology, 17, 1, 63-82 (2015) · Zbl 1327.26017 |
| [10] | Sarikaya, M. Z.; Budak, H., Generalized Ostrowski type inequalities for local fractional integrals, RGMIA Research Report Collection, 18 (2015) · Zbl 1390.26036 |
| [11] | Sarikaya, M. Z.; Erden, S.; Budak, H., Some generalized Ostrowski type inequalities involving local fractional integrals and applications, Advances in Inequalities and Applications, 6 (2016) · Zbl 1538.26080 |
| [12] | Sarikaya, M. Z.; Erden, S.; Budak, H., Some integral inequalities for local fractional integrals, RGMIA Research Report Collection, 18 (2015) |
| [13] | Sarikaya, M. Z.; Budak, H.; Erden, S., On new inequalities of Simpson’s type for generalized convex functions, RGMIA Research Report Collection, 18 (2015) |
| [14] | Yang, X. J., Advanced Local Fractional Calculus and Its Applications (2012) |
| [15] | Yang, J.; Baleanu, D.; Yang, X. J., Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys. (2013) · Zbl 1291.35123 |
| [16] | Yang, X. J., Local fractional integral equations and their applications, Advances in Computer Science and its Applications (ACSA), 1, 4 (2012) |
| [17] | Yang, X. J., Generalized local fractional Taylor’s formula with local fractional derivative, Journal of Expert Systems, 1, 1, 26-30 (2012) |
| [18] | Yang, X. J., Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications, 1, 1, 12-16 (2012) |
| [19] | Yang, X. J.; Baleanu, D.; Srivastava, H. M., Local Fractional Integral Transforms and their Applications (2016) · Zbl 1336.44001 |
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