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SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS

Yıl 2016, Cilt: 4 Sayı: 2, 70 - 78, 01.10.2016

Öz

In this paper, we establish some new inequalities for differentiable mappings whose derivatives in absolute value are $s-$convex in the second sense. These results are connected with the celebrated Hermite-Hadamard-Fejer type integral inequality.

Kaynakça

  • [1] S.S. Dragomir and S. Fitzpatrik, The Hadamard's inequality for s-convex functions in the second sense, Demons. Math., 32(4) (1999), 687-696.
  • [2] M. Bombardelli, S. Varosanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejer inequalities, Comp. Math. App., 58 (2009), 1869-1877.
  • [3] P. Cerone, S.S. Dragomir and C.E.M. Pearce, A generalized trapezoid inequality for functions of bounded variation, Turkish J. Math. 24 (2000), 147-163.
  • [4] S.S. Dragomir, Tow mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl. 167 (1992), 49-56.
  • [5] S.S. Dragomir, Hermite-Hadamard's type inequalities for operator convexs functions, Appl. Math. Comp. 218 (2011), 766-772.
  • [6] S.S. Dragomir, P. Cerone and A. Sofo, Some remarks on the trapezoid rule in numerical integration, Indian J. Pure Appl. Math. 31 (2000), 475-494.
  • [7] S.S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA monographs, Victoria University, 2000. [Online: http://ajmaa.org/RGMIA/monographs.php].
  • [8] L. Fejer, Ueber die Fourierreihen, II, Math. Naturwiss. Anz Ungar. Akad., Wiss, 24 (1906), 369-390,
  • [9] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100{111.
  • [10] I. Iscan, E. Set and M.E. Ozdemir, On new general integral inequalities for s-convex functions, Appl. Math. Comp. 246 (2004), 306-315. [11] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and the midpoint formula, Appl. Math. Comp. 147 (2004), 137-146.
  • [12] U.S. Kirmaci, M.E.  Ozdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 153(2) (2004), 361-368.
  • [13] U. Kirmaci, M. Bakula, M.E.  Ozdemir and J. Pecaric, Hadamard-tpye inequalities for s-convex functions, Appl. Math. Comp., 193 (2007), 26{35.
  • [14] M. E. Ozdemir, C. Yildiz, A.O. Akdemir and E. Set, On some inequalities for s-convex functions and applications, Jour. Ineq. and App., (2013), 2013:333.
  • [15] M.Z. Sarikaya and M.E. Kiris, Some New Inequalities of Hermite-Hadamard Type for s-Convex Functions, Miskolc Math. Notes, 16(1) (2015), 491{501.
  • [16] M.Z. Sarikaya, E. Set and M.E.  Ozdemir, On new inequalities of simpson's type for s􀀀convex functions, Comput. Math. Appl., 60(8) (2010), 2191{2199, .
  • [17] E. Set, I. Iscan and F. Zehir, On Some New Inequalities of Hermite-Hadamard Type Involving Harmonically Convex Functions Via Fractional Integrals, Konuralp Jour. Math., 3(1) (2015), 42{55.
  • [18] E. Set, _I. _ Iscan, M.Z. Sarkaya and M.E.  Ozdemir, On new inequalities of Hermite-Hadamard- Fejer type for convex functions via fractional integrals, Appl. Math. Comp. 259 (2015), 875- 881.
  • [19] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapezoidal formula, Taiwanese J. of Math. 15(4) (2011), 1737-1747.
  • [20] K.-L. Tseng, S.R. Hwang and S.S. Dragomir, On some new inequalities of Hermite-Hadamard- Fejer type involving convex functions, Demons. Math. 40(1), (2007), 51{64.
  • [21] K.-L. Tseng, S.R. Hwang, S.S. Dragomir and Y.J. Cho, Fejer-Type Inequalities (I). Journ. Ineq. and Appl. (2010), doi:10.1155/2010/531976
  • [22] C . Yildiz, M.E.  Ozdemir and M. Gurbuz, On Some New Fejer Type Inequalities, Submitted.
  • [23] F. Qi, Z.-L. Yang, Generalizations and re nements of Hermite-Hadamard's inequality, The Rocky Mountain J. of Math. 35 (2005), 235-251.
  • [24] S.-H. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, The Rocky Mountain J. of Math. 39 (2009), 1741-1749.
Yıl 2016, Cilt: 4 Sayı: 2, 70 - 78, 01.10.2016

Öz

Kaynakça

  • [1] S.S. Dragomir and S. Fitzpatrik, The Hadamard's inequality for s-convex functions in the second sense, Demons. Math., 32(4) (1999), 687-696.
  • [2] M. Bombardelli, S. Varosanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejer inequalities, Comp. Math. App., 58 (2009), 1869-1877.
  • [3] P. Cerone, S.S. Dragomir and C.E.M. Pearce, A generalized trapezoid inequality for functions of bounded variation, Turkish J. Math. 24 (2000), 147-163.
  • [4] S.S. Dragomir, Tow mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl. 167 (1992), 49-56.
  • [5] S.S. Dragomir, Hermite-Hadamard's type inequalities for operator convexs functions, Appl. Math. Comp. 218 (2011), 766-772.
  • [6] S.S. Dragomir, P. Cerone and A. Sofo, Some remarks on the trapezoid rule in numerical integration, Indian J. Pure Appl. Math. 31 (2000), 475-494.
  • [7] S.S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA monographs, Victoria University, 2000. [Online: http://ajmaa.org/RGMIA/monographs.php].
  • [8] L. Fejer, Ueber die Fourierreihen, II, Math. Naturwiss. Anz Ungar. Akad., Wiss, 24 (1906), 369-390,
  • [9] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100{111.
  • [10] I. Iscan, E. Set and M.E. Ozdemir, On new general integral inequalities for s-convex functions, Appl. Math. Comp. 246 (2004), 306-315. [11] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and the midpoint formula, Appl. Math. Comp. 147 (2004), 137-146.
  • [12] U.S. Kirmaci, M.E.  Ozdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 153(2) (2004), 361-368.
  • [13] U. Kirmaci, M. Bakula, M.E.  Ozdemir and J. Pecaric, Hadamard-tpye inequalities for s-convex functions, Appl. Math. Comp., 193 (2007), 26{35.
  • [14] M. E. Ozdemir, C. Yildiz, A.O. Akdemir and E. Set, On some inequalities for s-convex functions and applications, Jour. Ineq. and App., (2013), 2013:333.
  • [15] M.Z. Sarikaya and M.E. Kiris, Some New Inequalities of Hermite-Hadamard Type for s-Convex Functions, Miskolc Math. Notes, 16(1) (2015), 491{501.
  • [16] M.Z. Sarikaya, E. Set and M.E.  Ozdemir, On new inequalities of simpson's type for s􀀀convex functions, Comput. Math. Appl., 60(8) (2010), 2191{2199, .
  • [17] E. Set, I. Iscan and F. Zehir, On Some New Inequalities of Hermite-Hadamard Type Involving Harmonically Convex Functions Via Fractional Integrals, Konuralp Jour. Math., 3(1) (2015), 42{55.
  • [18] E. Set, _I. _ Iscan, M.Z. Sarkaya and M.E.  Ozdemir, On new inequalities of Hermite-Hadamard- Fejer type for convex functions via fractional integrals, Appl. Math. Comp. 259 (2015), 875- 881.
  • [19] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapezoidal formula, Taiwanese J. of Math. 15(4) (2011), 1737-1747.
  • [20] K.-L. Tseng, S.R. Hwang and S.S. Dragomir, On some new inequalities of Hermite-Hadamard- Fejer type involving convex functions, Demons. Math. 40(1), (2007), 51{64.
  • [21] K.-L. Tseng, S.R. Hwang, S.S. Dragomir and Y.J. Cho, Fejer-Type Inequalities (I). Journ. Ineq. and Appl. (2010), doi:10.1155/2010/531976
  • [22] C . Yildiz, M.E.  Ozdemir and M. Gurbuz, On Some New Fejer Type Inequalities, Submitted.
  • [23] F. Qi, Z.-L. Yang, Generalizations and re nements of Hermite-Hadamard's inequality, The Rocky Mountain J. of Math. 35 (2005), 235-251.
  • [24] S.-H. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, The Rocky Mountain J. of Math. 39 (2009), 1741-1749.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

ÇETİN Yıldız

Yayımlanma Tarihi 1 Ekim 2016
Gönderilme Tarihi 9 Temmuz 2015
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Yıldız, Ç. (2016). SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS. Konuralp Journal of Mathematics, 4(2), 70-78.
AMA Yıldız Ç. SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS. Konuralp J. Math. Ekim 2016;4(2):70-78.
Chicago Yıldız, ÇETİN. “SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics 4, sy. 2 (Ekim 2016): 70-78.
EndNote Yıldız Ç (01 Ekim 2016) SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS. Konuralp Journal of Mathematics 4 2 70–78.
IEEE Ç. Yıldız, “SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS”, Konuralp J. Math., c. 4, sy. 2, ss. 70–78, 2016.
ISNAD Yıldız, ÇETİN. “SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics 4/2 (Ekim 2016), 70-78.
JAMA Yıldız Ç. SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS. Konuralp J. Math. 2016;4:70–78.
MLA Yıldız, ÇETİN. “SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics, c. 4, sy. 2, 2016, ss. 70-78.
Vancouver Yıldız Ç. SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS. Konuralp J. Math. 2016;4(2):70-8.
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