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HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Year 2016, Volume: 4 Issue: 1, 254 - 260, 01.04.2016

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].

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 s􀀀convex functions, Aequationes Math., 48 (1994) 100-111.
  • [8] U.S. Krmac Inequalities for di erentiable 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.
Year 2016, Volume: 4 Issue: 1, 254 - 260, 01.04.2016

Abstract

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 s􀀀convex functions, Aequationes Math., 48 (1994) 100-111.
  • [8] U.S. Krmac Inequalities for di erentiable 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.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Set

Mehmet Zeki Sarıkaya

Filiz Karakoç This is me

Publication Date April 1, 2016
Submission Date July 10, 2014
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Set, E., Sarıkaya, M. Z., & Karakoç, F. (2016). HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 4(1), 254-260.
AMA Set E, Sarıkaya MZ, Karakoç F. HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. April 2016;4(1):254-260.
Chicago Set, Erhan, Mehmet Zeki Sarıkaya, and Filiz Karakoç. “HERMITE-HADAMARD TYPE INEQUALITIES FOR H-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 254-60.
EndNote Set E, Sarıkaya MZ, Karakoç F (April 1, 2016) HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 1 254–260.
IEEE E. Set, M. Z. Sarıkaya, and F. Karakoç, “HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 4, no. 1, pp. 254–260, 2016.
ISNAD Set, Erhan et al. “HERMITE-HADAMARD TYPE INEQUALITIES FOR H-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/1 (April 2016), 254-260.
JAMA Set E, Sarıkaya MZ, Karakoç F. HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:254–260.
MLA Set, Erhan et al. “HERMITE-HADAMARD TYPE INEQUALITIES FOR H-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 254-60.
Vancouver Set E, Sarıkaya MZ, Karakoç F. HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(1):254-60.
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