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

Year 2016, Volume: 4 Issue: 3, 239 - 253, 30.09.2016

İmdat Iscan Mehmet Kunt Nazli Yazici

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

Hermite-Hadamard inequality Hermite-Hadamard-Fejér inequality Riemann-Liouville fractional integral

References

  • 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.
  • F. Chen and S. Wu, Fejér and Hermite-Hadamard type inqequalities for harmonically convex functions, Jurnal of applied Mathematics, volume 2014, article id:386806.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
  • L. Fejér, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
  • 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.
  • 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.
  • 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.
  • İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
  • İ. İşcan, On generalization of different type integral inequalities for s-convex functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 2(1) (2014), 55-67.
  • İ. İşcan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  • İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942
  • A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
  • M. A. Latif, S. S. Dragomir and E. Momoniat, Some Fejér type inequalities for harmonically-convex functions with applications to special means, http://rgmia.org/papers/v18/v18a24.pdf.
  • A. P. Prudnikov, Y. A. Brychkov, O. J. Marichev, Integral and series, Elementary Functions, vol. 1, Nauka, Moscow, 1981.
  • M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities, Stud. Univ. Babeş-Bolyai Math. 57(3) (2012), 377–386.
  • M.Z. Sarıkaya, E. Set, H. Yaldız and N. Başak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), 2403-2407.
  • K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejér inequality and weighted trapezoidal formula, Taiwanese journal of Mathematics, 15(4) (2011), 1737-1747.
  • J. Wang, X. Li, M. Fečkan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92(11) (2012), 2241-2253. doi:10.1080/00036811.2012.727986
  • J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013(325) (2013), 15 pages.

Year 2016, Volume: 4 Issue: 3, 239 - 253, 30.09.2016

İmdat Iscan Mehmet Kunt Nazli Yazici

Abstract

References

  • 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.
  • F. Chen and S. Wu, Fejér and Hermite-Hadamard type inqequalities for harmonically convex functions, Jurnal of applied Mathematics, volume 2014, article id:386806.
  • Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
  • L. Fejér, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
  • 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.
  • 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.
  • 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.
  • İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
  • İ. İşcan, On generalization of different type integral inequalities for s-convex functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 2(1) (2014), 55-67.
  • İ. İşcan, S. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014) 237-244.
  • İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (6) (2014), 935-942
  • A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006).
  • M. A. Latif, S. S. Dragomir and E. Momoniat, Some Fejér type inequalities for harmonically-convex functions with applications to special means, http://rgmia.org/papers/v18/v18a24.pdf.
  • A. P. Prudnikov, Y. A. Brychkov, O. J. Marichev, Integral and series, Elementary Functions, vol. 1, Nauka, Moscow, 1981.
  • M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities, Stud. Univ. Babeş-Bolyai Math. 57(3) (2012), 377–386.
  • M.Z. Sarıkaya, E. Set, H. Yaldız and N. Başak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9) (2013), 2403-2407.
  • K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejér inequality and weighted trapezoidal formula, Taiwanese journal of Mathematics, 15(4) (2011), 1737-1747.
  • J. Wang, X. Li, M. Fečkan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92(11) (2012), 2241-2253. doi:10.1080/00036811.2012.727986
  • J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013(325) (2013), 15 pages.
There are 19 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İmdat Iscan This is me

Mehmet Kunt

Nazli Yazici This is me

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

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.
AMA Iscan İ, Kunt M, Yazici N. Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals. New Trends in Mathematical Sciences. September 2016;4(3):239-253.
Chicago Iscan, İmdat, Mehmet Kunt, and Nazli Yazici. “Hermite-Hadamard-Fejér Type Inequalities for Harmonically Convex Functions via Fractional Integrals”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 239-53.
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 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, 2016.
ISNAD Iscan, İmdat et al. “Hermite-Hadamard-Fejér Type Inequalities for Harmonically Convex Functions via Fractional Integrals”. New Trends in Mathematical Sciences 4/3 (September 2016), 239-253.
JAMA 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, 2016, pp. 239-53.
Vancouver 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):239-53.
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