Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense

• Autorzy: Budak H. , Sarikaya M. Z. , Set E.

Identyfikatory

DOI

10.17512/jamcm.2016.4.02

• Języki publikacji: EN

Abstrakty

EN

In this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense.

Słowa kluczowe

EN

generalized Hermite-Hadamard inequality; generalized Hölder inequality; generalized convex functions

PL

nierówność Höldera; wypukłość funkcji; nierówność Hermite-Hadamarda

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 4
• Strony: 11--21
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Budak H.

• Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce-Turkey

autor

Sarikaya M. Z.

• Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce-Turkey

autor

Set E.

• Department of Mathematics, Faculty of Arts and Sciences, Ordu University, 52200, Ordu, Turkey

Bibliografia

• [1] Budak H., Sarikaya M.Z., Yildirim H., New inequalities for local fractional integrals, Iranian Journal of Science and Technology (Sciences), in press.
• [2] Chen G-S., Generalizations of Hölder's and some related integral inequalities on fractal space, Journal of Function Spaces and Applications Volume 2013, Article ID 198405.
• [3] Kılıçman A., Saleh W., Notions of generalized s-convex functions on fractal sets, Journal of Inequalities and Applications 2015, 312. 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, Article ID 636751, 7 pages.
• [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_(0 < _ < 1), arXiv:1506.07391v1 [math.CA].
• [8] Ostrowski A.M., Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 1938, 10, 226-227.
• [9] Saleh W., Kılıçman A., On generalized s-convex functions on fractal set, JP Journal of Geometry and Topology 2015, 17(1), 63-82.
• [10] Sarikaya M.Z., Budak H., Generalized Ostrowski type inequalities for local fractional integrals, RGMIA Research Report Collection 2015, 18, Article 62, 11 p.
• [11] Sarikaya M.Z., Erden S., Budak H., Some generalized Ostrowski type inequalities involving local fractional integrals and applications, Advances in Inequalities and Applications 2016, 6.
• [12] Sarikaya M.Z., Erden S., Budak H., Some integral inequalities for local fractional integrals, RGMIA Research Report Collection 2015, 18, Article 65, 12 p.
• [13] Sarikaya M.Z., Budak H., Erden S., On new inequalities of Simpson's type for generalized convex functions, RGMIA Research Report Collection 2015, 18, Article 66, 13 p.
• [14] Yang X.J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York 2012.
• [15] Yang J., Baleanu D., Yang X.J., Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys. 2013, Article ID 632309.
• [16] Yang X.J., Local fractional integral equations and their applications, Advances in Computer Science and its Applications (ACSA) 2012, 1(4).
• [17] Yang X.J., Generalized local fractional Taylor's formula with local fractional derivative, Journal of Expert Systems 2012, 1(1), 26-30.
• [18] Yang X.J., Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications 2012, 1(1), 12-16.
• [19] Yang X.J., Baleanu D., Srivastava H.M., Local Fractional Integral Transforms and their Applications, Elsevier, 2016.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.