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
Samet Erden
,
Mehmet Zeki Sarikaya
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
Samet Erden
,
Mehmet Zeki Sarikaya
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.