Research Article

Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals

Volume: 4 Number: 3 September 30, 2016
EN

Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals

Abstract

In this paper, firstly, Hermite-Hadamard-Fejér type inequality for harmonically convex functions in fractional integral forms have been established. Secondly, an integral identity and some Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions in fractional integral forms have been obtained. The some results presented here would provide extensions of those given in earlier works.


Keywords

References

  1. M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite Hadamard Fejér inequalities, Computers and Mathematics with Applications 58 (2009), 1869 1877.
  2. F. Chen and S. Wu, Fejér and Hermite-Hadamard type inqequalities for harmonically convex functions, Jurnal of applied Mathematics, volume 2014, article id:386806.
  3. Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
  4. L. Fejér, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
  5. J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
  6. İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math., 86(4) (2013), 727-746.
  7. İ. İşcan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1) (2014), 21-29 . doi: 10.1515/apam-2013-0029.
  8. İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

İmdat Iscan * This is me
Türkiye

Mehmet Kunt
Türkiye

Nazli Yazici This is me
Türkiye

Publication Date

September 30, 2016

Submission Date

June 3, 2016

Acceptance Date

July 21, 2016

Published in Issue

Year 1970 Volume: 4 Number: 3

APA
Iscan, İ., Kunt, M., & Yazici, N. (2016). Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences, 4(3), 239-253. https://izlik.org/JA29JL94AL
AMA
1.Iscan İ, Kunt M, Yazici N. Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences. 2016;4(3):239-253. https://izlik.org/JA29JL94AL
Chicago
Iscan, İmdat, Mehmet Kunt, and Nazli Yazici. 2016. “Hermite-Hadamard-Fejér Type Inequalities for Harmonically Convex Functions via Fractional Integrals”. New Trends in Mathematical Sciences 4 (3): 239-53. https://izlik.org/JA29JL94AL.
EndNote
Iscan İ, Kunt M, Yazici N (September 1, 2016) Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences 4 3 239–253.
IEEE
[1]İ. Iscan, M. Kunt, and N. Yazici, “Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 239–253, Sept. 2016, [Online]. Available: https://izlik.org/JA29JL94AL
ISNAD
Iscan, İmdat - Kunt, Mehmet - Yazici, Nazli. “Hermite-Hadamard-Fejér Type Inequalities for Harmonically Convex Functions via Fractional Integrals”. New Trends in Mathematical Sciences 4/3 (September 1, 2016): 239-253. https://izlik.org/JA29JL94AL.
JAMA
1.Iscan İ, Kunt M, Yazici N. Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences. 2016;4:239–253.
MLA
Iscan, İmdat, et al. “Hermite-Hadamard-Fejér Type Inequalities for Harmonically Convex Functions via Fractional Integrals”. New Trends in Mathematical Sciences, vol. 4, no. 3, Sept. 2016, pp. 239-53, https://izlik.org/JA29JL94AL.
Vancouver
1.İmdat Iscan, Mehmet Kunt, Nazli Yazici. Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences [Internet]. 2016 Sep. 1;4(3):239-53. Available from: https://izlik.org/JA29JL94AL