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Year 2016, Volume: 4 Issue: 2, 102 - 109, 30.10.2016
https://doi.org/10.36753/mathenot.421462

Abstract

References

  • es [1] L. Fejér, Uber die Fourierreihen, II. Math. Naturwise. Anz Ungar. Akad., Wiss 24 (1906), 369-390, (in Hungarian).
  • [2] 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.
  • [3] İ. İşcan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint arXiv:1404.7722 (2014).
  • [4] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals. Applicable Analysis(2013), doi: 10.1080/00036811.2013.851785.
  • [5] İ. İşcan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals. J. Inequal. Appl. (2013), 2013(491).
  • [6] 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.
  • [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier. Amsterdam, 2006.
  • [8] M. Kunt, İ. İşcan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex functions via fractional integrals. RGMIA Research Report Collection 18(2015), Article 108, 12 pp.
  • [9] M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometricallyarithmetically-convex functions with applications. RGMIA Research Report Collection 18(2015), Article 25,18pp.
  • [10] C. P. Niculescu, Convexity according to the geometric mean. Math. Inequal. Appl. 3 (2) (2000), 155-167. Available online at http://dx.doi.org/10.7153/mia-03-19.
  • [11] C. P. Niculescu, Convexity according to means. Math. Inequal. Appl. 6 (4) (2003), 571-579. Available online at http://dx.doi.org/10.7153/mia-06-53.
  • [12] M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities. Stud. Univ. Babe¸s-Bolyai Math. 57(3) (2012), 377–386.
  • [13] Erhan Set, İ. İşcan, M. Zeki Sarikaya, M. Emin Ozdemir, On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals. Applied Mathematics and Computation 259 (2015) 875–881.
  • [14] 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.
  • [15] 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) (2012), 2241-2253. doi:10.1080/00036811.2012.727986.
  • [16] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means. J. Inequal. Appl. (2013), 2013(325), 15 pages.

On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals

Year 2016, Volume: 4 Issue: 2, 102 - 109, 30.10.2016
https://doi.org/10.36753/mathenot.421462

Abstract

In this paper, new Hermite-Hadamard-Fejer type integral inequalities for quasi-geometrically convex
functions in fractional integral forms are obtained. 

References

  • es [1] L. Fejér, Uber die Fourierreihen, II. Math. Naturwise. Anz Ungar. Akad., Wiss 24 (1906), 369-390, (in Hungarian).
  • [2] 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.
  • [3] İ. İşcan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint arXiv:1404.7722 (2014).
  • [4] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals. Applicable Analysis(2013), doi: 10.1080/00036811.2013.851785.
  • [5] İ. İşcan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals. J. Inequal. Appl. (2013), 2013(491).
  • [6] 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.
  • [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations. Elsevier. Amsterdam, 2006.
  • [8] M. Kunt, İ. İşcan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex functions via fractional integrals. RGMIA Research Report Collection 18(2015), Article 108, 12 pp.
  • [9] M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometricallyarithmetically-convex functions with applications. RGMIA Research Report Collection 18(2015), Article 25,18pp.
  • [10] C. P. Niculescu, Convexity according to the geometric mean. Math. Inequal. Appl. 3 (2) (2000), 155-167. Available online at http://dx.doi.org/10.7153/mia-03-19.
  • [11] C. P. Niculescu, Convexity according to means. Math. Inequal. Appl. 6 (4) (2003), 571-579. Available online at http://dx.doi.org/10.7153/mia-06-53.
  • [12] M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities. Stud. Univ. Babe¸s-Bolyai Math. 57(3) (2012), 377–386.
  • [13] Erhan Set, İ. İşcan, M. Zeki Sarikaya, M. Emin Ozdemir, On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals. Applied Mathematics and Computation 259 (2015) 875–881.
  • [14] 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.
  • [15] 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) (2012), 2241-2253. doi:10.1080/00036811.2012.727986.
  • [16] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means. J. Inequal. Appl. (2013), 2013(325), 15 pages.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mehmet Kunt

İmdat İşcan

Publication Date October 30, 2016
Submission Date July 22, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Kunt, M., & İşcan, İ. (2016). On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Mathematical Sciences and Applications E-Notes, 4(2), 102-109. https://doi.org/10.36753/mathenot.421462
AMA Kunt M, İşcan İ. On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Math. Sci. Appl. E-Notes. October 2016;4(2):102-109. doi:10.36753/mathenot.421462
Chicago Kunt, Mehmet, and İmdat İşcan. “On New Inequalities of Hermite-Hadamard-Fejer Type for Quasi-Geometrically Convex Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes 4, no. 2 (October 2016): 102-9. https://doi.org/10.36753/mathenot.421462.
EndNote Kunt M, İşcan İ (October 1, 2016) On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Mathematical Sciences and Applications E-Notes 4 2 102–109.
IEEE M. Kunt and İ. İşcan, “On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 102–109, 2016, doi: 10.36753/mathenot.421462.
ISNAD Kunt, Mehmet - İşcan, İmdat. “On New Inequalities of Hermite-Hadamard-Fejer Type for Quasi-Geometrically Convex Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes 4/2 (October 2016), 102-109. https://doi.org/10.36753/mathenot.421462.
JAMA Kunt M, İşcan İ. On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016;4:102–109.
MLA Kunt, Mehmet and İmdat İşcan. “On New Inequalities of Hermite-Hadamard-Fejer Type for Quasi-Geometrically Convex Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, 2016, pp. 102-9, doi:10.36753/mathenot.421462.
Vancouver Kunt M, İşcan İ. On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016;4(2):102-9.

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