GENERALIZED FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FORm CONVEX AND ( ; m) CONVEX FUNCTIONS

Year 2018, Volume: 67 Issue: 1, 333 - 344, 01.02.2018

Erhan Set Barış Çelik

https://doi.org/10.1501/Commua1_0000000855

Cited By: 4

Keywords

m convex function, (, m) convex function, Hermite-Hadamard inequality, fractional integral operator

References

• Agarwal, R.P., Luo, M.-J., and Raina, R.K., On Ostrowski type inequalities, Fasciculi Math- ematici, 204 (2016), 5-27.
• Alomari, M., and Darus, M., On the Hadamard’s inequality for log-convex functions on the coordinates, Journal of Inequalities and Applications, vol. 2009, Article ID 283147, 13 pages
• Azpeitia, A.G., Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.
• Bakula, M.K., Özdemir, M.E., Peµcari´c, J., Hadamard tpye inequalities for m convex and ( ; m)-convex functions, J. Ineq. Pure and Appl. Math., 9(4) (2008), Art. 96.
• Bakula, M.K., and Peµcari´c, J., Note on some Hadamard-type inequalities, Journal of Inequal- ities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, 2004.
• Chen, F., On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity, Chinese J. Math., Article ID 173923, 7 pages, 2014.
• Dragomir, S.S., and Pearce, C.E.M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
• Dragomir, S.S., On some new inequalities of Hermite-Hadamard type for m convex func- tions, Tamkang J. Math., 3(1) (2002).
• Mihesan, V.G., A Generalization of the Convexity, Seminar of Functional Equations, Ap- prox. and Convex, Cluj-Napoca, Romania, 1993.
• Özdemir, M.E., Avci, M. and Set, E., On some inequalities of Hermite-Hadamard type via m-convexity, Applied Mathematics Letters, vol. 23, no. 9, pp. 1065–1070, 2010.
• Peµcari´c, J.E., Proschan, F., Tong, Y.L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
• Raina, R.K., On generalized Wright’s hypergeometric functions and fractional calculus oper- ators, East Asian Math. J., 21(2) (2005), 191-203.
• Set, E., Özdemir, M.E. and Dragomir, S.S., On the Hermite-Hadamard inequality and other integral inequalities involving two functions, Journal of Inequalities and Applications, Article ID 148102, 9 pages, 2010.
• Set, E., Özdemir, M.E. and Dragomir, S.S., On Hadamard-Type inequalities involving several kinds of convexity, Journal of Inequalities and Applications, Article ID 286845, 12 pages, 2010. new Set, E., Choi, J., Çelik, B., A approach integral ResearchGate, Hadamard https://www.researchgate.net/publication/313437121. using fractional operator
• Set, E., Noor, M.A., Awan, M.U., Gözpınar, A., Some new generalized Hermite-Hadamard type inequalities for convex functions involving fractional integral operators, Journal of In- equalities and Applications, 2017:169; http://dx.doi.org/10.1186/s13660-017-1444-6 (2017).
• Toader, G., Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation And Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1985, 329-338.
• Usta, F., Budak, H., Sarıkaya, M.Z. and Set, E., On generalization of trapezoid type inequal- ities for s-convex functions with generalized fractional integral operators, Filomat, accepted for publication. Yaldız, H., Sarıkaya, M.Z., On the Hermite-Hadamard type inequalities for fractional integral operator, ResearchGate, https://www.researchgate.net/publication/309824275.
• Current address : Erhan SET: Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey E-mail address : [e-mail] ORCID: orcid.org/0000-0003-1364-5396
• Current address : Barı¸s ÇEL·IK: Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey E-mail address : [e-mail] ORCID: orcid.org/0000-0001-5372-7543