PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On Hermite-Hadamard type inequalities for s-convex mappings via fractional integrals of a function with respect to another function

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we obtain some Hermite-Hadamard type inequalities for s-convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.
Rocznik
Tom
Strony
25--36
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
  • Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
  • Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Bibliografia
  • [1] Azpeitia A.G., Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28(1994), 7-12.
  • [2] Bakula M.K., Pečarić J., Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, 5(3)(2004), Art. 74.
  • [3] Belarbi S., Dahmani Z., On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3)(2009), Art. 86.
  • [4] Breckner W.W., Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23(1978), 13-20.
  • [5] Dahmani Z., New inequalities in fractional integrals, International Journal of Nonlinear Science, 9(4)(2010), 493-497.
  • [6] Dahmani Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58.
  • [7] Dahmani Z., Tabharit L., Taf S., Some fractional integral inequalities, Nonl. Sci. Lett. A, 1(2)(2010), 155-160.
  • [8] Dahmani Z. Tabharit L., Taf S., New generalizations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3)(2010), 93-99.
  • [9] Deng J., Wang J., Fractional Hermite-Hadamard inequalities for (α,m)-logarithmically convex functions, J. Inequal. Appl. 2013, Article ID 364 (2013).
  • [10] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • [11] Dragomir S.S., Agarwal R.P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11(5)(1998), 91-95.
  • [12] Gorenflo R., Mainardi F., Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  • [13] Hudzik H., Maligranda L., Some remarks on s-convex functions, Aequationes Math., 48(1994), 100-111.
  • [14] Jleli M., Samet B., On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function, J. Nonlinear Sci. Appl., 9(2016), 1252-1260.
  • [15] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam, 2006.
  • [16] Miller S., Ross B., An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, USA, 1993, p. 2.
  • [17] Pečarić J.E., Proschan F., Tong Y.L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • [18] Podlubni I., Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [19] Sarikaya M.Z., Ogunmez H., On new inequalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, Volume 2012 (2012), Article ID 428983, 10 pages.
  • [20] Sarikaya M.Z., Set E., Yaldiz H., Basak N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048, 57(2013), 2403-2407.
  • [21] Sarikaya M.Z., Filiz H., Kiris M.E., On some generalized integral inequalities for Riemann-Liouville fractional integrals, Filomat, 29(6)(2015), 1307-1314, DOI 10.2298/FIL1506307S.
  • [22] Sarikaya M.Z., Budak H., Generalized Hermite-Hadamard type integral inequalities for functions whose 3rd derivatives are s-convex, Tbilisi Mathematical Journal, 7(2)(2014), 41-49.
  • [23] Sarikaya M.Z., Kiris M.E., Some new inequalities of Hermite-Hadamard type for s-convex functions, Miskolc Mathematical Notes, 16(1)(2015), 491-501.
  • [24] Sarikaya M.Z., Budak H., Some Hermite-Hadamard type integral inequalities for twice differentiable mappings via fractional integrals, Facta Universitatis Ser:. Math. Inform., 29(4)(2014), 371-384.
  • [25] Set E., Sarikaya M.Z., Ozdemir M.E., Yildirim H., The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results, JAMSI, 10(2)(2014), 69-83.
  • [26] Tunc M., On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat, 27(4)(2013), 559-565.
  • [27] Zhang Y., Wang J., On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, J. Inequal. Appl. 2013, Article ID 220(2013).
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-778d4f78-c515-46f5-8e12-65cc9b2c1c23
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.