Research Article
BibTex RIS Cite
Year 2019, Volume: 68 Issue: 1, 61 - 69, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443617

Abstract

References

  • Agarwal, R.P., Luo M.J. and Raina, R.K., On Ostrowski type inequalities, Fasciculi Mathematici, 204 (2016), 5-27.
  • Hermite, C., Sur deux limites d'une integrale definie, Mathesis, 3, 82 (1883).
  • İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. Doi: 10.15672/HJMS.2014437519.
  • İşcan, İ. and Wu, S., Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Applied Mathematics and Computation 238, (2014) 237-244 .
  • Kirane, M. and Torebek B.T., Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via fractional integrals, arXiv:1701.00092v1 [math.FA] (2016).
  • Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).
  • Raina, R.K., On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191-203.
  • Sarıkaya, M.Z., Set, E., Yaldız, H. and Başak, N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. 57(9-10), (2013) 2403-2407.
  • Set, E. and Gözpınar, A., Some new inequalities involving generalized fractional integral operators for several class of functions, AIP Conference Proceedings, 1833, 020038 (2017); doi: 10.1063/1.4981686.
  • Set, E. and Gözpınar, A., Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators, Topol. Algebra Appl, 5 (2017) 55--62.
  • Set, E., Akdemir, A.O. and Çelik, B., On Generalization of Fejér Type Inequalities via fractional integral operator, ResearchGate, https://www.researchgate.net/publication/311452467.
  • Set, E. and Çelik, B., On generalization related to the left side of Fejér's inequalites via fractional integral operator, ResearchGate, https://www.researchgate.net/publication/311651826.
  • Set, E., Choi, J. and Çelik, B., Certain Hermite-Hadamard type inequality involving generalized fractional integral operators, RACSAM, Doi: 10.1007/s13398-017-0444-1.
  • Usta, F., Budak, H., Sarıkaya M.Z. and Set, E., On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, accepted.
  • Yaldız H. and Sarıkaya, M.Z., On the Hermite-Hadamard type inequalities for fractional integral operator, ResearchGate, https://www.researchgate.net/publication/309824275.

Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals

Year 2019, Volume: 68 Issue: 1, 61 - 69, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443617

Abstract

The object of this paper is to obtain certain Hermite-Hadamard type integral inequalities involving general class of fractional integral operators and the fractional integral operators with exponential kernel by using harmonically convex functions

References

  • Agarwal, R.P., Luo M.J. and Raina, R.K., On Ostrowski type inequalities, Fasciculi Mathematici, 204 (2016), 5-27.
  • Hermite, C., Sur deux limites d'une integrale definie, Mathesis, 3, 82 (1883).
  • İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. Doi: 10.15672/HJMS.2014437519.
  • İşcan, İ. and Wu, S., Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Applied Mathematics and Computation 238, (2014) 237-244 .
  • Kirane, M. and Torebek B.T., Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via fractional integrals, arXiv:1701.00092v1 [math.FA] (2016).
  • Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).
  • Raina, R.K., On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191-203.
  • Sarıkaya, M.Z., Set, E., Yaldız, H. and Başak, N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. 57(9-10), (2013) 2403-2407.
  • Set, E. and Gözpınar, A., Some new inequalities involving generalized fractional integral operators for several class of functions, AIP Conference Proceedings, 1833, 020038 (2017); doi: 10.1063/1.4981686.
  • Set, E. and Gözpınar, A., Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators, Topol. Algebra Appl, 5 (2017) 55--62.
  • Set, E., Akdemir, A.O. and Çelik, B., On Generalization of Fejér Type Inequalities via fractional integral operator, ResearchGate, https://www.researchgate.net/publication/311452467.
  • Set, E. and Çelik, B., On generalization related to the left side of Fejér's inequalites via fractional integral operator, ResearchGate, https://www.researchgate.net/publication/311651826.
  • Set, E., Choi, J. and Çelik, B., Certain Hermite-Hadamard type inequality involving generalized fractional integral operators, RACSAM, Doi: 10.1007/s13398-017-0444-1.
  • Usta, F., Budak, H., Sarıkaya M.Z. and Set, E., On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, accepted.
  • Yaldız H. and Sarıkaya, M.Z., On the Hermite-Hadamard type inequalities for fractional integral operator, ResearchGate, https://www.researchgate.net/publication/309824275.
There are 15 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Erhan Set 0000-0003-1364-5396

M. Emin Özdemir 0000-0002-5992-094X

Necla Korkut This is me 0000-0003-1294-567X

Publication Date February 1, 2019
Submission Date May 23, 2017
Acceptance Date November 5, 2017
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Set, E., Özdemir, M. E., & Korkut, N. (2019). Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 61-69. https://doi.org/10.31801/cfsuasmas.443617
AMA Set E, Özdemir ME, Korkut N. Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):61-69. doi:10.31801/cfsuasmas.443617
Chicago Set, Erhan, M. Emin Özdemir, and Necla Korkut. “Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 61-69. https://doi.org/10.31801/cfsuasmas.443617.
EndNote Set E, Özdemir ME, Korkut N (February 1, 2019) Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 61–69.
IEEE E. Set, M. E. Özdemir, and N. Korkut, “Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 61–69, 2019, doi: 10.31801/cfsuasmas.443617.
ISNAD Set, Erhan et al. “Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 61-69. https://doi.org/10.31801/cfsuasmas.443617.
JAMA Set E, Özdemir ME, Korkut N. Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:61–69.
MLA Set, Erhan et al. “Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 61-69, doi:10.31801/cfsuasmas.443617.
Vancouver Set E, Özdemir ME, Korkut N. Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):61-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.