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ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Year 2015, Volume: 3 Issue: 1, 42 - 55, 01.04.2015

Erhan Set , İmdat İşcan , Fatma Zehır

Abstract

In this paper, some new results related to the left-hand side of the Hermite-Hadamard type inequality for harmonically convex functions using Riemann Liouville fractional integrals are obtained.

Keywords

Harmonically convex function Hermite-Hadamard type inequality Riemann Liouville fractional integrals

References

  • [1] R.Goren o, F.Mainardi, "Fractionalcalculus;integral and di erentiable equations of fractional order", Springer Verlag, Wien,1997,p.223-276
  • [2] S.G.Samko, A.A.Kilbas, O.I.Marichev, "Fractional Integrals and Derivates Theory and Ap-plication ,Gordon and Breach Science", New York,1993
  • [3] İ. İşcan and S. Wu, "Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals",Appl. Math. Compt., 238 (2014), 237-244.
  • [4] İ. İşcan, "Hermite-Hadamard type inequalities for harmonically convex functions", Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  • [5] İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis: An Int. J., 93 (9) (2014), 1846{1862.
  • [6] İ. İşcan, "New general integral inequalities for quasi-geometrically convex functions via fractional integrals", J. Inequal. Appl., 2013(491), 15 pages, 2013.
  • [7] A. A. Kilbas, H.M. Srivastava HM and J.J. Trujillo, Theory and applications of fractional differential equations, Amsterdam, Elsevier, 2006.
  • [8] A. P. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, 1981.
  • [9] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, "Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities", Math. Comput. Model., 57, 2403-2407, 2013.
  • [10] E. Set, "New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals", Comput. Math. Appl., 63, 1147-1154, 2012.
  • [11] J. Wang, X. Li, M. Feckan and Y. Zhou, "Hermite-Hadamard-type inequalities for Riemann Liouville fractional integrals via two kinds of convexity", Appl. Anal., 92(11), 2241-2253, 2012.
  • [12] J. Wang, C. Zhu and Y. Zhou, "New generalized Hermite-Hadamard type inequalities and applications to special means", J. Inequal. Appl., 2013(325), 15 pages, 2013.

Year 2015, Volume: 3 Issue: 1, 42 - 55, 01.04.2015

Erhan Set , İmdat İşcan , Fatma Zehır

Abstract

References

  • [1] R.Goren o, F.Mainardi, "Fractionalcalculus;integral and di erentiable equations of fractional order", Springer Verlag, Wien,1997,p.223-276
  • [2] S.G.Samko, A.A.Kilbas, O.I.Marichev, "Fractional Integrals and Derivates Theory and Ap-plication ,Gordon and Breach Science", New York,1993
  • [3] İ. İşcan and S. Wu, "Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals",Appl. Math. Compt., 238 (2014), 237-244.
  • [4] İ. İşcan, "Hermite-Hadamard type inequalities for harmonically convex functions", Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  • [5] İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis: An Int. J., 93 (9) (2014), 1846{1862.
  • [6] İ. İşcan, "New general integral inequalities for quasi-geometrically convex functions via fractional integrals", J. Inequal. Appl., 2013(491), 15 pages, 2013.
  • [7] A. A. Kilbas, H.M. Srivastava HM and J.J. Trujillo, Theory and applications of fractional differential equations, Amsterdam, Elsevier, 2006.
  • [8] A. P. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, 1981.
  • [9] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, "Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities", Math. Comput. Model., 57, 2403-2407, 2013.
  • [10] E. Set, "New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals", Comput. Math. Appl., 63, 1147-1154, 2012.
  • [11] J. Wang, X. Li, M. Feckan and Y. Zhou, "Hermite-Hadamard-type inequalities for Riemann Liouville fractional integrals via two kinds of convexity", Appl. Anal., 92(11), 2241-2253, 2012.
  • [12] J. Wang, C. Zhu and Y. Zhou, "New generalized Hermite-Hadamard type inequalities and applications to special means", J. Inequal. Appl., 2013(325), 15 pages, 2013.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Set

İmdat İşcan

Fatma Zehır This is me

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Set, E., İşcan, İ., & Zehır, F. (2015). ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 3(1), 42-55.
AMA Set E, İşcan İ, Zehır F. ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. April 2015;3(1):42-55.
Chicago Set, Erhan, İmdat İşcan, and Fatma Zehır. “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 42-55.
EndNote Set E, İşcan İ, Zehır F (April 1, 2015) ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 3 1 42–55.
IEEE E. Set, İ. İşcan, and F. Zehır, “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 3, no. 1, pp. 42–55, 2015.
ISNAD Set, Erhan et al. “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 3/1 (April 2015), 42-55.
JAMA Set E, İşcan İ, Zehır F. ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2015;3:42–55.
MLA Set, Erhan et al. “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 42-55.
Vancouver Set E, İşcan İ, Zehır F. ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2015;3(1):42-55.
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