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Year 2018, Volume: 6 Issue: 1, 35 - 41, 15.04.2018

Mehmet Zeki Sarıkaya Fatma Ertuğral Fatma Yıldırım

Abstract

References

  • [1] W. W. Breckner, Stetigkeitsaussagen f¨ur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23(1978), 13-20.
  • [2] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
  • [3] J. Deng and J. Wang, Fractional Hermite-Hadamard inequalities for (a;m)-logarithmically convex functions, Journal of Inequalities and Applications 2013, 2013:364.
  • [4] S. S. Dragomir and S. Fitzpatrik, The Hadamard’s inequality for s-convex functions in the second sense, Demonstration Math. 32(4), (1999), 687-696.
  • [5] S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.
  • [6] S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • [7] L. Fejer, U¨ ber die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369–390. (Hungarian).
  • [8] I. Iscan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint arXiv: 1404. 7722 (2014).
  • [9] J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.
  • [10] M. Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048, 57 (2013) 2403–2407.
  • [11] M. Z. Sarikaya and S. Erden, On the weigted integral inequalities for convex functions, Acta Universitatis Sapientiae Mathematica, 6, 2 (2014) 194-208.
  • [12] M. Z. Sarikaya and S. Erden, On The Hermite- Hadamard-Fejer Type Integral Inequality for Convex Function, Turkish Journal of Analysis and Number Theory, 2014, Vol. 2, No. 3, 85-89.
  • [13] M. Z. Sarikaya, On new Hermite Hadamard Fejer Type integral inequalities, Studia Universitatis Babes-Bolyai Mathematica., 57(2012), No. 3, 377-386.
  • [14] K-L. Tseng, G-S. Yang and K-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapozidal formula, Taiwanese J. Math. 15(4), pp:1737-1747, 2011.
  • [15] C.-L. Wang, X.-H. Wang, On an extension of Hadamard inequality for convex functions, Chin. Ann. Math. 3 (1982) 567–570.
  • [16] S.-H. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, The Rocky Mountain J. of Math., vol. 39, no. 5, pp. 1741–1749, 2009.
  • [17] M. Tunc, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27:4 (2013), 559–565.
  • [18] 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. (2012). doi:10.1080/00036811.2012.727986.
  • [19] B-Y, Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat.. 42(3), 243–257 (2013).
  • [20] B-Y, Xi and F. Qi, Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl.. 18(2), 163–176 (2013)
  • [21] Y. Zhang and J-R. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, Journal of Inequalities and Applications 2013, 2013:220.
  • [22] Y-M. Liao, J-H Deng and J-R Wang, Riemann-Liouville fractional Hermite-Hadamard inequalities. Part I: for once differentiable geometricarithmetically s-convex functions, Journal of Inequalities and Applications 2013, 2013:443.

On the Hermite-Hadamard-Fejér type integral inequality for s-convex function

Year 2018, Volume: 6 Issue: 1, 35 - 41, 15.04.2018

Mehmet Zeki Sarıkaya Fatma Ertuğral Fatma Yıldırım

Abstract

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard-Fejér type inequality for functions whose first derivatives absolute values are s-convex.The results presented here would provide extensions of those given in earlier works.



Keywords

Hermite-Hadamard inequality s-convex function Hölder Inequality

References

  • [1] W. W. Breckner, Stetigkeitsaussagen f¨ur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23(1978), 13-20.
  • [2] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
  • [3] J. Deng and J. Wang, Fractional Hermite-Hadamard inequalities for (a;m)-logarithmically convex functions, Journal of Inequalities and Applications 2013, 2013:364.
  • [4] S. S. Dragomir and S. Fitzpatrik, The Hadamard’s inequality for s-convex functions in the second sense, Demonstration Math. 32(4), (1999), 687-696.
  • [5] S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.
  • [6] S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • [7] L. Fejer, U¨ ber die Fourierreihen, II. Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369–390. (Hungarian).
  • [8] I. Iscan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint arXiv: 1404. 7722 (2014).
  • [9] J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.
  • [10] M. Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048, 57 (2013) 2403–2407.
  • [11] M. Z. Sarikaya and S. Erden, On the weigted integral inequalities for convex functions, Acta Universitatis Sapientiae Mathematica, 6, 2 (2014) 194-208.
  • [12] M. Z. Sarikaya and S. Erden, On The Hermite- Hadamard-Fejer Type Integral Inequality for Convex Function, Turkish Journal of Analysis and Number Theory, 2014, Vol. 2, No. 3, 85-89.
  • [13] M. Z. Sarikaya, On new Hermite Hadamard Fejer Type integral inequalities, Studia Universitatis Babes-Bolyai Mathematica., 57(2012), No. 3, 377-386.
  • [14] K-L. Tseng, G-S. Yang and K-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapozidal formula, Taiwanese J. Math. 15(4), pp:1737-1747, 2011.
  • [15] C.-L. Wang, X.-H. Wang, On an extension of Hadamard inequality for convex functions, Chin. Ann. Math. 3 (1982) 567–570.
  • [16] S.-H. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, The Rocky Mountain J. of Math., vol. 39, no. 5, pp. 1741–1749, 2009.
  • [17] M. Tunc, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27:4 (2013), 559–565.
  • [18] 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. (2012). doi:10.1080/00036811.2012.727986.
  • [19] B-Y, Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat.. 42(3), 243–257 (2013).
  • [20] B-Y, Xi and F. Qi, Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl.. 18(2), 163–176 (2013)
  • [21] Y. Zhang and J-R. Wang, On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals, Journal of Inequalities and Applications 2013, 2013:220.
  • [22] Y-M. Liao, J-H Deng and J-R Wang, Riemann-Liouville fractional Hermite-Hadamard inequalities. Part I: for once differentiable geometricarithmetically s-convex functions, Journal of Inequalities and Applications 2013, 2013:443.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Zeki Sarıkaya

Fatma Ertuğral This is me

Fatma Yıldırım This is me

Publication Date April 15, 2018
Submission Date April 10, 2018
Acceptance Date April 16, 2018
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Sarıkaya, M. Z., Ertuğral, F., & Yıldırım, F. (2018). On the Hermite-Hadamard-Fejér type integral inequality for s-convex function. Konuralp Journal of Mathematics, 6(1), 35-41.
AMA Sarıkaya MZ, Ertuğral F, Yıldırım F. On the Hermite-Hadamard-Fejér type integral inequality for s-convex function. Konuralp J. Math. April 2018;6(1):35-41.
Chicago Sarıkaya, Mehmet Zeki, Fatma Ertuğral, and Fatma Yıldırım. “On the Hermite-Hadamard-Fejér Type Integral Inequality for S-Convex Function”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 35-41.
EndNote Sarıkaya MZ, Ertuğral F, Yıldırım F (April 1, 2018) On the Hermite-Hadamard-Fejér type integral inequality for s-convex function. Konuralp Journal of Mathematics 6 1 35–41.
IEEE M. Z. Sarıkaya, F. Ertuğral, and F. Yıldırım, “On the Hermite-Hadamard-Fejér type integral inequality for s-convex function”, Konuralp J. Math., vol. 6, no. 1, pp. 35–41, 2018.
ISNAD Sarıkaya, Mehmet Zeki et al. “On the Hermite-Hadamard-Fejér Type Integral Inequality for S-Convex Function”. Konuralp Journal of Mathematics 6/1 (April 2018), 35-41.
JAMA Sarıkaya MZ, Ertuğral F, Yıldırım F. On the Hermite-Hadamard-Fejér type integral inequality for s-convex function. Konuralp J. Math. 2018;6:35–41.
MLA Sarıkaya, Mehmet Zeki et al. “On the Hermite-Hadamard-Fejér Type Integral Inequality for S-Convex Function”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 35-41.
Vancouver Sarıkaya MZ, Ertuğral F, Yıldırım F. On the Hermite-Hadamard-Fejér type integral inequality for s-convex function. Konuralp J. Math. 2018;6(1):35-41.
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