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On the Hermite-Hadamard's and Ostrowski's inequalities for the co-ordinated convex functions

Year 2017, Volume: 5 Issue: 3, 33 - 45, 01.07.2017

Abstract

In this paper, we give new some inequalities of Hermite-Hadamard's and Ostrowski's type for convex functions on the co-ordinates defined in a rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the co-ordinates on the rectangle from the plane.

References

  • M. Alomari andM. Darus, Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sciences, 3 (32) (2008), 1557-1567.
  • M. Alomari and M. Darus, On the Hadamard’s inequality for log-convex functions on the coordinates, J. of Inequal. and Appl, Article ID 283147, (2009), 13 pages.
  • N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality for double integrals and applications for cubature formulae, Soochow J. Math., 27 (1), (2001), 109-114.
  • P. Cerone and S. S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Math., 37 (2004), no. 2, 299-308.
  • F. Chen, On Hermite-Hadamard type inequalities for s-convex functions on the coordinates via Riemann-Liouville fractional integrals, Journal of Applied Mathematics, Volume 2014, Article ID 248710, 8 pages.
  • S. S. Dragomir, On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 4 (2001), 775-788.
  • J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58 (1893), 171–215.
  • M. A. Latif, S. Hussain and S. S. Dragomir, New Ostrowski type inequalities for co-ordinated convex functions, TJMM, 4 (2012), No. 2, 125-136.
  • M. A. Latif and M. Alomari, Hadamard-type inequalities for product two convex functions on the co-ordinetes, Int. Math. Forum, 4(47), 2009, 2327-2338.
  • M. A. Latif and M. Alomari, On the Hadamard-type inequalities for h-convex functions on the co-ordinetes, Int. J. of Math. Analysis, 3(33), 2009, 1645-1656.
  • M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, Journal of Inequalities and Applications 2012, 2012:28.
  • A.M. Ostrowski, ¨Uber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938), 226-227.
  • M. E. Ozdemir, E. Set and M. Z. Sarikaya, New some Hadamard’s type inequalities for coordinated m-convex and (a,m)-convex functions, Hacettepe Journal of Mathematics and Statistics , 40(2), 2011, 219-229.
  • J. Park, Generalizations of the Simpson-like type inequalities for co-ordinated s-convex mappings in the second sense, International Journal of Mathematics and Mathematical Sciences Volume 2012, Article ID 715751, 16 pages.
  • J. Park, Some Hadamard’s type inequalities for co-ordinated (s;m)-convex mappings in the second sense, Far East Journal of Mathematical Sciences, vol. 51, no. 2, pp. 205–216, 2011.
  • M. Z. Sarikaya, E. Set, M. E. ¨Ozdemir and S. S. Dragomir, New some Hadamard’s type inequalities for co-ordineted convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2) (2012) 137-152.
  • M. Z. Sarikaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, Vol. 25, No. 2, 134-147, 2014.
  • M. Z. Sarikaya, Some inequalities for differentiable co-ordinated convex mappings, Asian-European Journal of Mathematics, Vol: 08, 1550058 (2015), 21 pages.
  • M. Z. Sarikaya and H. Ogunmez, On the weighted Ostrowski type integral inequality for double integrals, The Arabian Journal for Science and Engineering (AJSE)-Mathematics, (2011) 36: 1153-1160.
  • M. Zeki Sarikaya and M. K. Yıldız, On the Generalized Montgomery Identity for Double Integrals, Dynamics of Continuous, Discrete and Impulsive Systems-Series A, Mathematical Analysis, in press.
Year 2017, Volume: 5 Issue: 3, 33 - 45, 01.07.2017

Abstract

References

  • M. Alomari andM. Darus, Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities, Int. J. Contemp. Math. Sciences, 3 (32) (2008), 1557-1567.
  • M. Alomari and M. Darus, On the Hadamard’s inequality for log-convex functions on the coordinates, J. of Inequal. and Appl, Article ID 283147, (2009), 13 pages.
  • N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality for double integrals and applications for cubature formulae, Soochow J. Math., 27 (1), (2001), 109-114.
  • P. Cerone and S. S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Math., 37 (2004), no. 2, 299-308.
  • F. Chen, On Hermite-Hadamard type inequalities for s-convex functions on the coordinates via Riemann-Liouville fractional integrals, Journal of Applied Mathematics, Volume 2014, Article ID 248710, 8 pages.
  • S. S. Dragomir, On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 4 (2001), 775-788.
  • J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58 (1893), 171–215.
  • M. A. Latif, S. Hussain and S. S. Dragomir, New Ostrowski type inequalities for co-ordinated convex functions, TJMM, 4 (2012), No. 2, 125-136.
  • M. A. Latif and M. Alomari, Hadamard-type inequalities for product two convex functions on the co-ordinetes, Int. Math. Forum, 4(47), 2009, 2327-2338.
  • M. A. Latif and M. Alomari, On the Hadamard-type inequalities for h-convex functions on the co-ordinetes, Int. J. of Math. Analysis, 3(33), 2009, 1645-1656.
  • M. A. Latif and S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, Journal of Inequalities and Applications 2012, 2012:28.
  • A.M. Ostrowski, ¨Uber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938), 226-227.
  • M. E. Ozdemir, E. Set and M. Z. Sarikaya, New some Hadamard’s type inequalities for coordinated m-convex and (a,m)-convex functions, Hacettepe Journal of Mathematics and Statistics , 40(2), 2011, 219-229.
  • J. Park, Generalizations of the Simpson-like type inequalities for co-ordinated s-convex mappings in the second sense, International Journal of Mathematics and Mathematical Sciences Volume 2012, Article ID 715751, 16 pages.
  • J. Park, Some Hadamard’s type inequalities for co-ordinated (s;m)-convex mappings in the second sense, Far East Journal of Mathematical Sciences, vol. 51, no. 2, pp. 205–216, 2011.
  • M. Z. Sarikaya, E. Set, M. E. ¨Ozdemir and S. S. Dragomir, New some Hadamard’s type inequalities for co-ordineted convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2) (2012) 137-152.
  • M. Z. Sarikaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, Vol. 25, No. 2, 134-147, 2014.
  • M. Z. Sarikaya, Some inequalities for differentiable co-ordinated convex mappings, Asian-European Journal of Mathematics, Vol: 08, 1550058 (2015), 21 pages.
  • M. Z. Sarikaya and H. Ogunmez, On the weighted Ostrowski type integral inequality for double integrals, The Arabian Journal for Science and Engineering (AJSE)-Mathematics, (2011) 36: 1153-1160.
  • M. Zeki Sarikaya and M. K. Yıldız, On the Generalized Montgomery Identity for Double Integrals, Dynamics of Continuous, Discrete and Impulsive Systems-Series A, Mathematical Analysis, in press.
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Samet Erden

Mehmet Zeki Sarikaya This is me

Publication Date July 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Erden, S., & Sarikaya, M. Z. (2017). On the Hermite-Hadamard’s and Ostrowski’s inequalities for the co-ordinated convex functions. New Trends in Mathematical Sciences, 5(3), 33-45.
AMA Erden S, Sarikaya MZ. On the Hermite-Hadamard’s and Ostrowski’s inequalities for the co-ordinated convex functions. New Trends in Mathematical Sciences. July 2017;5(3):33-45.
Chicago Erden, Samet, and Mehmet Zeki Sarikaya. “On the Hermite-Hadamard’s and Ostrowski’s Inequalities for the Co-Ordinated Convex Functions”. New Trends in Mathematical Sciences 5, no. 3 (July 2017): 33-45.
EndNote Erden S, Sarikaya MZ (July 1, 2017) On the Hermite-Hadamard’s and Ostrowski’s inequalities for the co-ordinated convex functions. New Trends in Mathematical Sciences 5 3 33–45.
IEEE S. Erden and M. Z. Sarikaya, “On the Hermite-Hadamard’s and Ostrowski’s inequalities for the co-ordinated convex functions”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 33–45, 2017.
ISNAD Erden, Samet - Sarikaya, Mehmet Zeki. “On the Hermite-Hadamard’s and Ostrowski’s Inequalities for the Co-Ordinated Convex Functions”. New Trends in Mathematical Sciences 5/3 (July 2017), 33-45.
JAMA Erden S, Sarikaya MZ. On the Hermite-Hadamard’s and Ostrowski’s inequalities for the co-ordinated convex functions. New Trends in Mathematical Sciences. 2017;5:33–45.
MLA Erden, Samet and Mehmet Zeki Sarikaya. “On the Hermite-Hadamard’s and Ostrowski’s Inequalities for the Co-Ordinated Convex Functions”. New Trends in Mathematical Sciences, vol. 5, no. 3, 2017, pp. 33-45.
Vancouver Erden S, Sarikaya MZ. On the Hermite-Hadamard’s and Ostrowski’s inequalities for the co-ordinated convex functions. New Trends in Mathematical Sciences. 2017;5(3):33-45.