Research Article
BibTex RIS Cite

On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions

Year 2019, Volume: 68 Issue: 1, 734 - 750, 01.02.2019

Sercan Turhan İmdat İşcan

https://doi.org/10.31801/cfsuasmas.464205
Cited By: 1

Abstract

In this paper, we give the theorems and results for the trapezoidal and midpoint type inequality of new Hermite-Hadamard-Fejér for harmonically-quasi convex functions via fractional integrals.

Keywords

Harmonically-Quasi-convex Hermite-Hadamard-Fejer type inequalities fractional Integral

References

  • Alomari, M. W., Darus, M., Kirmaci, U. S., Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Computers and Mathematics with Applications, 59 (2010), 225-232.
  • Chen, F. and Wu, S., Fejér and Hermite-Hadamard type inqequalities for harmonically convex functions, J. Appl. Math., volume 2014, article id:386806.
  • İşcan, İ., Wu, S. , Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  • İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  • İşcan, İ. and Kunt, M., Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals, RGMIA, 18(2015), Article 107, 16 pp.
  • İşcan, İ. and Kunt, M., Hermite-Hadamard-Fejér type inequalities for harmonically quasi-convex functions via fractional integrals, KYUNGPOOK Math., accepted paper.
  • İşcan, İ., Turhan, S. and Maden, S., Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral, NTMSCI 4 (2016), No. 2, 1-10.
  • Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006.
  • Latif, M. A., Dragomir, S. S. and Momoniat, E., Some Fejér type inequalities for harmonically-convex functions with applications to special means, RGMIA, 18(2015), Article 24, 17 pp.
  • Park, J., Hermite-Hadamard Type Inequalities for Harmonically Quasi-Convex Functions (I), Applied Mathematical Sciences, Vol. 8, (2014), no. 99, 4917-4925.
  • Park, J. , Hermite-Hadamard Type Inequalities for Harmonically Quasi-convex Functions (II), International Journal of Mathematical Analysis Vol. 8, (2014), no. 33, 1605-1614.
  • Turhan, S. and İşcan, İ., Some New Hermite-Hadamard-Fejer Type Inequalities For Harmonically Convex Functions, Researchgate, doi: 10.13140/RG.2.1.2842.3765, under review.
  • Zhang, T.-Y., Ji, A.-P. and Qi, F., Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions. Proc. Jangjeon Math. Soc, 16(3) (2013), 399-407.

Year 2019, Volume: 68 Issue: 1, 734 - 750, 01.02.2019

Sercan Turhan İmdat İşcan

https://doi.org/10.31801/cfsuasmas.464205
Cited By: 1

Abstract

References

  • Alomari, M. W., Darus, M., Kirmaci, U. S., Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Computers and Mathematics with Applications, 59 (2010), 225-232.
  • Chen, F. and Wu, S., Fejér and Hermite-Hadamard type inqequalities for harmonically convex functions, J. Appl. Math., volume 2014, article id:386806.
  • İşcan, İ., Wu, S. , Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  • İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
  • İşcan, İ. and Kunt, M., Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals, RGMIA, 18(2015), Article 107, 16 pp.
  • İşcan, İ. and Kunt, M., Hermite-Hadamard-Fejér type inequalities for harmonically quasi-convex functions via fractional integrals, KYUNGPOOK Math., accepted paper.
  • İşcan, İ., Turhan, S. and Maden, S., Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral, NTMSCI 4 (2016), No. 2, 1-10.
  • Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006.
  • Latif, M. A., Dragomir, S. S. and Momoniat, E., Some Fejér type inequalities for harmonically-convex functions with applications to special means, RGMIA, 18(2015), Article 24, 17 pp.
  • Park, J., Hermite-Hadamard Type Inequalities for Harmonically Quasi-Convex Functions (I), Applied Mathematical Sciences, Vol. 8, (2014), no. 99, 4917-4925.
  • Park, J. , Hermite-Hadamard Type Inequalities for Harmonically Quasi-convex Functions (II), International Journal of Mathematical Analysis Vol. 8, (2014), no. 33, 1605-1614.
  • Turhan, S. and İşcan, İ., Some New Hermite-Hadamard-Fejer Type Inequalities For Harmonically Convex Functions, Researchgate, doi: 10.13140/RG.2.1.2842.3765, under review.
  • Zhang, T.-Y., Ji, A.-P. and Qi, F., Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions. Proc. Jangjeon Math. Soc, 16(3) (2013), 399-407.
There are 13 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Sercan Turhan 0000-0002-4392-2182

İmdat İşcan 0000-0001-6749-0591

Publication Date February 1, 2019
Submission Date July 19, 2017
Acceptance Date April 9, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Turhan, S., & İşcan, İ. (2019). On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 734-750. https://doi.org/10.31801/cfsuasmas.464205
AMA Turhan S, İşcan İ. On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):734-750. doi:10.31801/cfsuasmas.464205
Chicago Turhan, Sercan, and İmdat İşcan. “On New Hermite-Hadamard-Fejér Type Inequalities for Harmonically Quasi Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 734-50. https://doi.org/10.31801/cfsuasmas.464205.
EndNote Turhan S, İşcan İ (February 1, 2019) On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 734–750.
IEEE S. Turhan and İ. İşcan, “On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 734–750, 2019, doi: 10.31801/cfsuasmas.464205.
ISNAD Turhan, Sercan - İşcan, İmdat. “On New Hermite-Hadamard-Fejér Type Inequalities for Harmonically Quasi Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 734-750. https://doi.org/10.31801/cfsuasmas.464205.
JAMA Turhan S, İşcan İ. On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:734–750.
MLA Turhan, Sercan and İmdat İşcan. “On New Hermite-Hadamard-Fejér Type Inequalities for Harmonically Quasi Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 734-50, doi:10.31801/cfsuasmas.464205.
Vancouver Turhan S, İşcan İ. On New Hermite-Hadamard-Fejér type inequalities for harmonically quasi convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):734-50.

Cited By

The right Riemann–Liouville fractional Hermite–Hadamard type inequalities derived from Green’s function
AIP Advances
https://doi.org/10.1063/1.5143908

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.