Hermite–Hadamard type inequalities for F –convex functions involving generalized fractional integrals
DOI:
https://doi.org/10.24193/subbmath.2022.1.11Keywords:
Hermite–Hadamard inequality, F –convex, general fractional integral.Abstract
In this paper, we firstly summarize some properties of the family F and F –convex functions which are defined by B. Samet. Utilizing generalized fractional integrals new Hermite–Hadamard type inequalities for F –convex functions have been provided. Some results given earlier works are also as special cases of our results.
Mathematics Subject Classification (2010): 26A51, 26A33, 26D07, 26D10, 26D15.
Received 15 August 2019; Accepted 17 January 2020.
References
Ali, M.A., Budak, H., Abbas, M., Sarikaya, M.Z., Kashuri, A., Hermite–Hadamard type inequalities for h–convex functions via generalized fractional integrals, Submitted, (2019).
Budak, H., Sarikaya, M.Z., On Ostrowski type inequalities for F-convex function, AIP Conference Proceedings, 1833, 020057 (2017), doi: 10.1063/1.4981705.
Budak, H., Sarikaya, M.Z., Yildiz, M.K., Hermite-Hadamard type inequalities for F-convex function involving fractional integrals, Filomat, 32(2018), no. 16, 5509-5518.
Budak, H., Tunc¸, T., Sarikaya, M.Z., On Hermite-Hadamard type inequalities for F-convex functions, Miskolc Math. Notes, 20(2019), no. 1, 169-191.
Defnetti, B., Sulla strati cazioni convesse, Ann. Math. Pura. Appl., 30(1949), 173-183.
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(1998), no. 5, 91-95.
Dragomir, S.S., Pearce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
Gorenflo, R., Mainardi, F., Fractional Calculus: Integral and Differential Equations of Fractional Order, Springer Verlag, Wien, 1997, 223-276.
Hudzik, H., Maligranda, L., Some remarks on s-convex functions, Aequationes Math., 48(1994), 100-111.
Hyers, D.H., Ulam, S.M., Approximately convex functions, Proc. Amer. Math. Soc., 3(1952), 821-828.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, 2006.
Kirmaci, U.S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147(2004), 91-95.
Mangasarian, O.L., Pseudo-convex functions, SIAM Journal on Control., 3(1965), 281- 290.
Miller, S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, USA, 1993.
Mohammed, P.O., Sarikaya, M.Z., Hermite-Hadamard type inequalities for F -convex function involving fractional integrals, J. Inequal. Appl., 2018(2018), Art. no. 359.
Pearce, C.E.M., Pecaric, J., Inequalities for differentiable mappings with application to special means and quadrature formula, Appl. Math. Lett., 13(2000), 51-55.
Pecaric, J.E., Proschan, F., Tong, Y.L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
Podlubni, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
Polyak, B.T., Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl., 7(1966), 72-75.
Samet, B., On an implicit convexity concept and some integral inequalities, J. Inequal. Appl., 2016(2016), Art. no. 308.
Sarikaya, M.Z., Aktan, N., On the generalization some integral inequalities and their applications, Math. Comput. Modelling, 54(2011), no. 9-10, 2175-2182.
Sarikaya, M.Z., Ertugral, F., On the generalized Hermite-Hadamard inequalities, Annals of the University of Craiova – Mathematics and Computer Science Series (in press).
Sarikaya, M.Z., Saglam, A., Yildirim, H., On some Hadamard-type inequalities for h−convex functions, J. Math. Inequal., 2(2008), no. 3, 335-341.
Sarikaya, M.Z., Saglam, A., Yildirim, H., New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex, Int. J. Open Probl. Comput. Sci. Math., IJOPCM, 5(2012), no. 3, 1-14.
Sarikaya, M.Z., Set, E., Yaldiz, H., Basak, N., Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modelling, 57(2013), 2403-2407.
Sarikaya, M.Z., Tunc¸, T., Budak, H., Simpson’s type inequality for F-convex function, Facta Univ., Ser. Math. Inf., 32(2018), no. 5, 747-753.
Set, E., Mumcu, I., Hermite-Hadamard type inequalities for F-convex functions via Katugampola fractional integral, (submitted), (2018).
Varosanec, S., On h-convexity, J. Math. Anal. Appl., 326(2007), no. 1, 303-311.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
