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ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES

Year 2015, Volume: 3 Issue: 2, 77 - 88, 01.10.2015

B. Meftah K. Boukerrıoua

Abstract

The aim of this paper is to establish some new Cebysev type inequalities involving functions whose mixed partial derivatives are (h1; h2)- convex on the co-ordinates.

Keywords

Cebysev type inequalities co-ordinates (h1; h2)-convex integral inequality

References

  • [1] Ahmad, F., Barnett, N. S., & Dragomir, S. S. (2009). New weighted Ostrowski and Cebysev type inequalities. Nonlinear Analysis: Theory, Methods & Applications, 71(12), e1408-e1412.
  • [2] Alomari, M., & Darus, M. (2008). The Hadamard's inequality for s-convex function of 2- variables on the co-ordinates. International Journal of Math. Analysis, 2(13), 629-638.
  • [3] Boukerrioua, K., Guezane-Lakoud, A.(2007). On generalization of Cebysev type inequalities. J. Inequal. Pure Appl. Math. 8,2, Art 55.
  • [4] Chebyshev, P. L. (1882). Sur les expressions approximatives des integrales de nies par les autres prises entre les m^emes limites. InProc.Math.Soc.Charkov(Vol.2,pp.93-98):
  • [5] Dragomir, S. S. (2001). On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J Math. 4, 775{788.
  • [6] Guazene-Lakoud, A. and Aissaoui, F.2011. New Cebysev type inequalities for double integrals, J. Math. Inequal, 5(4) , 453{462.
  • [7] Latif, M. A., & Alomari, M. (2009). On Hadamard-type inequalities for h-convex functions on the co-ordinates. International Journal of Math. Analysis, 3(33), 1645-1656.
  • [8] Pachpatte, B. G., & Talkies, N. A. (2006). On Cebysev type inequalities involving functions whose derivatives belong to Lp spaces. J. Inequal. Pure and Appl. Math, 7(2), Art 58.
  • [9] Pachaptte, B. G. (2003). On some inequalities for convex functions,RGMIA Res.Rep.Coll, 6.
  • [10] Pachpatte, B. G. (2006). On Cebysev-Gruss type inequalities via Pecaric's extension of the Montgomery identity. JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only], 7(1), Art 11 .
  • [11] Sarikaya, M.Z., Budak, H., Yaldiz, H. (2014). Some New Ostrowski Type Inequalities for Co-Ordinated Convex Functions." Turkish Journal of Analysis and Number Theory, vol. 2, no. 5 (2014).
  • [12] Sarikaya, M.Z., Budak, H., Yaldiz, H. Cebysev type inequalities for co-ordinated convex functions. Pure and Applied Mathematics Letters 2(2014)44-48.

Year 2015, Volume: 3 Issue: 2, 77 - 88, 01.10.2015

B. Meftah K. Boukerrıoua

Abstract

References

  • [1] Ahmad, F., Barnett, N. S., & Dragomir, S. S. (2009). New weighted Ostrowski and Cebysev type inequalities. Nonlinear Analysis: Theory, Methods & Applications, 71(12), e1408-e1412.
  • [2] Alomari, M., & Darus, M. (2008). The Hadamard's inequality for s-convex function of 2- variables on the co-ordinates. International Journal of Math. Analysis, 2(13), 629-638.
  • [3] Boukerrioua, K., Guezane-Lakoud, A.(2007). On generalization of Cebysev type inequalities. J. Inequal. Pure Appl. Math. 8,2, Art 55.
  • [4] Chebyshev, P. L. (1882). Sur les expressions approximatives des integrales de nies par les autres prises entre les m^emes limites. InProc.Math.Soc.Charkov(Vol.2,pp.93-98):
  • [5] Dragomir, S. S. (2001). On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane. Taiwanese J Math. 4, 775{788.
  • [6] Guazene-Lakoud, A. and Aissaoui, F.2011. New Cebysev type inequalities for double integrals, J. Math. Inequal, 5(4) , 453{462.
  • [7] Latif, M. A., & Alomari, M. (2009). On Hadamard-type inequalities for h-convex functions on the co-ordinates. International Journal of Math. Analysis, 3(33), 1645-1656.
  • [8] Pachpatte, B. G., & Talkies, N. A. (2006). On Cebysev type inequalities involving functions whose derivatives belong to Lp spaces. J. Inequal. Pure and Appl. Math, 7(2), Art 58.
  • [9] Pachaptte, B. G. (2003). On some inequalities for convex functions,RGMIA Res.Rep.Coll, 6.
  • [10] Pachpatte, B. G. (2006). On Cebysev-Gruss type inequalities via Pecaric's extension of the Montgomery identity. JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only], 7(1), Art 11 .
  • [11] Sarikaya, M.Z., Budak, H., Yaldiz, H. (2014). Some New Ostrowski Type Inequalities for Co-Ordinated Convex Functions." Turkish Journal of Analysis and Number Theory, vol. 2, no. 5 (2014).
  • [12] Sarikaya, M.Z., Budak, H., Yaldiz, H. Cebysev type inequalities for co-ordinated convex functions. Pure and Applied Mathematics Letters 2(2014)44-48.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

B. Meftah This is me

K. Boukerrıoua

Publication Date October 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Meftah, B., & Boukerrıoua, K. (2015). ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES. Konuralp Journal of Mathematics, 3(2), 77-88.
AMA Meftah B, Boukerrıoua K. ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES. Konuralp J. Math. October 2015;3(2):77-88.
Chicago Meftah, B., and K. Boukerrıoua. “ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; H2)-CONVEX ON THE CO-ORDINATES”. Konuralp Journal of Mathematics 3, no. 2 (October 2015): 77-88.
EndNote Meftah B, Boukerrıoua K (October 1, 2015) ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES. Konuralp Journal of Mathematics 3 2 77–88.
IEEE B. Meftah and K. Boukerrıoua, “ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES”, Konuralp J. Math., vol. 3, no. 2, pp. 77–88, 2015.
ISNAD Meftah, B. - Boukerrıoua, K. “ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; H2)-CONVEX ON THE CO-ORDINATES”. Konuralp Journal of Mathematics 3/2 (October 2015), 77-88.
JAMA Meftah B, Boukerrıoua K. ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES. Konuralp J. Math. 2015;3:77–88.
MLA Meftah, B. and K. Boukerrıoua. “ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; H2)-CONVEX ON THE CO-ORDINATES”. Konuralp Journal of Mathematics, vol. 3, no. 2, 2015, pp. 77-88.
Vancouver Meftah B, Boukerrıoua K. ON SOME CEBYSEV TYPE INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE (h1; h2)-CONVEX ON THE CO-ORDINATES. Konuralp J. Math. 2015;3(2):77-88.
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