HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS
Year 2016,
Volume: 4 Issue: 1, 254 - 260, 01.04.2016
Erhan Set
,
Mehmet Zeki Sarıkaya
,
Filiz Karakoç
Abstract
By making use of identity of the established by Sarkaya [4], some new Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral are established. Our results are the generalizations of the results obtain by Sarkaya [4].
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integrals and related fractional inequalities Mathematical and Computer Modelling, 57 (2013)
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fractional integrals, Konuralp Journal of Mathematics, 1 (1) (2013) 48-53.
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(;m)convex functions via fractional integrals, (submitted).
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the second sense via fractional integrals, Comp. Math. Appl., 63(7) (2012), 1147-1154.
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Year 2016,
Volume: 4 Issue: 1, 254 - 260, 01.04.2016
Erhan Set
,
Mehmet Zeki Sarıkaya
,
Filiz Karakoç
References
- [1] W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in
topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), 13-20.
- [2] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure Appl.
Math. 10 (3) (2009) Art. 86.
- [3] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 9 (4) (2010) 493{
497.
- [4] Z. Dahmani, On Minkowski and Hermite{Hadamard integral inequalities via fractional integration,
Ann. Funct. Anal. 1 (1) (2010) 51{58.
- [5] Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonlinear. Sci. Lett.
A 1 (2) (2010) 155{160.
- [6] S.S. Dragomir J.Pecaric and L.E.Persson, Some inequalities of Hadamard type, Soochow J.
Math 21 (1995), 335-241.
- [7] H.Hudzik, L.Maligranda, Some remarks on sconvex functions, Aequationes Math., 48 (1994)
100-111.
- [8] U.S. Krmac Inequalities for dierentiable mappings and applicatons to special means of real
numbers and to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.
- [9] M.Z.Sarkaya Hermite-Hadamard's inequalities for fractional integrals and related fractional
inequalities II (submitted).
- [10] M.Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann{Liouville fractional integration,
Abstract and Applied Analysis, Volume 2012, Article ID 428983, 10 pages,
doi:10.1155/2012/428983.
- [11] M.Z. Sarikaya, E.Set, H.Yaldiz and N.Basak, Hermite-Hadamard's inequalities for fractional
integrals and related fractional inequalities Mathematical and Computer Modelling, 57 (2013)
2403-2407.
- [12] M.Z. Sarikaya and H. Yaldiz, On weighted Montogomery identities for Riemann-Liouville
fractional integrals, Konuralp Journal of Mathematics, 1 (1) (2013) 48-53.
- [13] E.Set, M.E. Ozdemir, M.Z. Sarkaya, F. Karakoc, Hermite-Hadamard type inequalities for
(;m)convex functions via fractional integrals, (submitted).
- [14] E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in
the second sense via fractional integrals, Comp. Math. Appl., 63(7) (2012), 1147-1154.
- [15] S.Varo^sanec, On h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311.