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Yıl 2018, Cilt: 6 Sayı: 1, 35 - 41, 15.04.2018

Mehmet Zeki Sarıkaya Fatma Ertuğral Fatma Yıldırım

Öz

Kaynakça

  • [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

Yıl 2018, Cilt: 6 Sayı: 1, 35 - 41, 15.04.2018

Mehmet Zeki Sarıkaya Fatma Ertuğral Fatma Yıldırım

Öz

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.



Anahtar Kelimeler

Hermite-Hadamard inequality s-convex function Hölder Inequality

Kaynakça

  • [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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Mehmet Zeki Sarıkaya

Fatma Ertuğral Bu kişi benim

Fatma Yıldırım Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2018
Gönderilme Tarihi 10 Nisan 2018
Kabul Tarihi 16 Nisan 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

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. Nisan 2018;6(1):35-41.
Chicago Sarıkaya, Mehmet Zeki, Fatma Ertuğral, ve Fatma Yıldırım. “On the Hermite-Hadamard-Fejér Type Integral Inequality for S-Convex Function”. Konuralp Journal of Mathematics 6, sy. 1 (Nisan 2018): 35-41.
EndNote Sarıkaya MZ, Ertuğral F, Yıldırım F (01 Nisan 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, ve F. Yıldırım, “On the Hermite-Hadamard-Fejér type integral inequality for s-convex function”, Konuralp J. Math., c. 6, sy. 1, ss. 35–41, 2018.
ISNAD Sarıkaya, Mehmet Zeki vd. “On the Hermite-Hadamard-Fejér Type Integral Inequality for S-Convex Function”. Konuralp Journal of Mathematics 6/1 (Nisan 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 vd. “On the Hermite-Hadamard-Fejér Type Integral Inequality for S-Convex Function”. Konuralp Journal of Mathematics, c. 6, sy. 1, 2018, ss. 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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