Year 2018,
Volume: 6 Issue: 1, 35 - 41, 15.04.2018
Mehmet Zeki Sarıkaya
,
Fatma Ertuğral
Fatma Yıldırım
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.
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.