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

Year 2016, Volume: 4 Issue: 2, 70 - 78, 01.10.2016

Abstract

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.

References

  • [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.
Year 2016, Volume: 4 Issue: 2, 70 - 78, 01.10.2016

Abstract

References

  • [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.
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

ÇETİN Yıldız

Publication Date October 1, 2016
Submission Date July 9, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

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. October 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, no. 2 (October 2016): 70-78.
EndNote Yıldız Ç (October 1, 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., vol. 4, no. 2, pp. 70–78, 2016.
ISNAD Yıldız, ÇETİN. “SOME NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR $s$-CONVEX FUNCTIONS”. Konuralp Journal of Mathematics 4/2 (October 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, vol. 4, no. 2, 2016, pp. 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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