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NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX

Year 2016, Volume: 4 Issue: 1, 1 - 22, 15.04.2016

Abstract

In this paper some Hermite-Hadamard type inequalities for convex functions of three variables on a rectangular box in $\mathbb{R}^3$ are given.

References

  • [1] A. Barani, S. Barani, Hermite-Hadamard inequalities for functions when a power of the absolute value of the rst derivative is P-convex, Bull. Aust. Math. Soc, 86 (2012), 126-134.
  • [2] A. Barani, A.G. Ghazanfari and S.S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl., 2012, 2012:247.
  • [3] S.S. Dragomir, Two re nements of Hadamard's inequalities, Coll. Pap. of the Fac. of Sci. Kragujevac (Yugoslavia) 11 (1990), 23-26. ZBL No. 729: 26017.
  • [4] S.S. Dragomir, A mapping in connection to Hadamard's inequality, An Ostro. Akad. Wiss. Math. -Natur (Wien) 128 (1991), 17-20. MR 93h: 26032. ZBL No. 747: 26015.
  • [5] S.S. Dragomir, On Hadamard's inequality for convex functions, Math. Balkanica., 6 (1992), 215-222. MR 934: 26033.
  • [6] S.S. Dragomir, A re nement of Hadamard's inequality for isotonic linear functionals, Tamkang J. Math., 24 (1993), 101-106.
  • [7] S.S. Dragomir, Two mappings in connection to Hadamard's inequality, J. Math. Anal. Appl. 167 (1992), 49-56. MR 93m: 26038. ZBL No. 758: 26014.
  • [8] S.S. Dragomir, Some re nements of Hadamard's inequalities, Gaz. Mat. Metod. (Romania) 11 (1990), 189-191.
  • [9] S.S. Dragomir, Some integral inequalities for differentiable convex functions, Contributions, Macedonian Acad. of sci. and arts., (Scopie) 16 (1992), 77-80.
  • [10] S.S. Dragomir, D.M. Milosevic and J. Sandor, On some re nements of Hadamard's inequalities and applications, Univ. Beograd, Publ. Elektrotelm. Fak., Ser. Mat., 4 (1993), 3-10.
  • [11] S.S. Dragomir, On the Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plan, Taiwan J. Math., 5 (2001), 775-778.
  • [12] A.G. Ghazanfari, A. Barani, Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions, Banach J. Math. Anal., 9 (2015), 9-20.
  • [13] M.A. Latif, Some inequalities for differentiable prequasiinvex functions with applications, KJM., 1 (2013), 17-29.
  • [14] M.E. Özdemir, A.O. Akdemir, Ç.Yıldız, On the co-ordinated convex functions, Appl. Math. Info. Sci., 8 (2014), 1085-1091.
  • [15] M.E. Özdemir, A.O. Akdemir, On some Hadamard-type inequalities for convex functions on a rectanfuler box, volume 2011, year 2011 article ID jnaa-00101, 10 pages doi:10.5899/2011/jnaa-00101
  • [16] J.E. Pecaric and S.S. Dragomir, On some integral inequalities for convex functions, Bull. Mat. Inst. Pol. Iasi, 36 (1990), 19-23.
  • [17] J.E. Pecaric and S.S. Dragomir, A generalization of Hadamard's inequality for isotonic linear functionals, Rodovi Math., (Sarajevo) 7 (1991), 103-107. 26026.
  • [18] M.Z. Sarıkaya, Erhan. Set, M.E. Özdemir and S.S. Dragomir, New some Hermite-Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences., 28 (2012), 137-152.
  • [19] D.Y. Wang, K.L. Tseng, G.S. Yang, Some Hadamard's inequality for co-ordinated convex functions in a rectangle from the plane, Taiwan J. Math., 11 (2007), 63-73.
  • [20] B-Y. Xi, J. Hua , F. Qi, Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle, Appl. Anal., 20 (2014), 29-39.
Year 2016, Volume: 4 Issue: 1, 1 - 22, 15.04.2016

Abstract

References

  • [1] A. Barani, S. Barani, Hermite-Hadamard inequalities for functions when a power of the absolute value of the rst derivative is P-convex, Bull. Aust. Math. Soc, 86 (2012), 126-134.
  • [2] A. Barani, A.G. Ghazanfari and S.S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl., 2012, 2012:247.
  • [3] S.S. Dragomir, Two re nements of Hadamard's inequalities, Coll. Pap. of the Fac. of Sci. Kragujevac (Yugoslavia) 11 (1990), 23-26. ZBL No. 729: 26017.
  • [4] S.S. Dragomir, A mapping in connection to Hadamard's inequality, An Ostro. Akad. Wiss. Math. -Natur (Wien) 128 (1991), 17-20. MR 93h: 26032. ZBL No. 747: 26015.
  • [5] S.S. Dragomir, On Hadamard's inequality for convex functions, Math. Balkanica., 6 (1992), 215-222. MR 934: 26033.
  • [6] S.S. Dragomir, A re nement of Hadamard's inequality for isotonic linear functionals, Tamkang J. Math., 24 (1993), 101-106.
  • [7] S.S. Dragomir, Two mappings in connection to Hadamard's inequality, J. Math. Anal. Appl. 167 (1992), 49-56. MR 93m: 26038. ZBL No. 758: 26014.
  • [8] S.S. Dragomir, Some re nements of Hadamard's inequalities, Gaz. Mat. Metod. (Romania) 11 (1990), 189-191.
  • [9] S.S. Dragomir, Some integral inequalities for differentiable convex functions, Contributions, Macedonian Acad. of sci. and arts., (Scopie) 16 (1992), 77-80.
  • [10] S.S. Dragomir, D.M. Milosevic and J. Sandor, On some re nements of Hadamard's inequalities and applications, Univ. Beograd, Publ. Elektrotelm. Fak., Ser. Mat., 4 (1993), 3-10.
  • [11] S.S. Dragomir, On the Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plan, Taiwan J. Math., 5 (2001), 775-778.
  • [12] A.G. Ghazanfari, A. Barani, Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions, Banach J. Math. Anal., 9 (2015), 9-20.
  • [13] M.A. Latif, Some inequalities for differentiable prequasiinvex functions with applications, KJM., 1 (2013), 17-29.
  • [14] M.E. Özdemir, A.O. Akdemir, Ç.Yıldız, On the co-ordinated convex functions, Appl. Math. Info. Sci., 8 (2014), 1085-1091.
  • [15] M.E. Özdemir, A.O. Akdemir, On some Hadamard-type inequalities for convex functions on a rectanfuler box, volume 2011, year 2011 article ID jnaa-00101, 10 pages doi:10.5899/2011/jnaa-00101
  • [16] J.E. Pecaric and S.S. Dragomir, On some integral inequalities for convex functions, Bull. Mat. Inst. Pol. Iasi, 36 (1990), 19-23.
  • [17] J.E. Pecaric and S.S. Dragomir, A generalization of Hadamard's inequality for isotonic linear functionals, Rodovi Math., (Sarajevo) 7 (1991), 103-107. 26026.
  • [18] M.Z. Sarıkaya, Erhan. Set, M.E. Özdemir and S.S. Dragomir, New some Hermite-Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences., 28 (2012), 137-152.
  • [19] D.Y. Wang, K.L. Tseng, G.S. Yang, Some Hadamard's inequality for co-ordinated convex functions in a rectangle from the plane, Taiwan J. Math., 11 (2007), 63-73.
  • [20] B-Y. Xi, J. Hua , F. Qi, Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle, Appl. Anal., 20 (2014), 29-39.
There are 20 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

A. Baranı

F. Malmır This is me

Publication Date April 15, 2016
Submission Date October 18, 2017
Acceptance Date October 4, 2015
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Baranı, A., & Malmır, F. (2016). NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX. Konuralp Journal of Mathematics, 4(1), 1-22.
AMA Baranı A, Malmır F. NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX. Konuralp J. Math. April 2016;4(1):1-22.
Chicago Baranı, A., and F. Malmır. “NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 1-22.
EndNote Baranı A, Malmır F (April 1, 2016) NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX. Konuralp Journal of Mathematics 4 1 1–22.
IEEE A. Baranı and F. Malmır, “NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX”, Konuralp J. Math., vol. 4, no. 1, pp. 1–22, 2016.
ISNAD Baranı, A. - Malmır, F. “NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX”. Konuralp Journal of Mathematics 4/1 (April 2016), 1-22.
JAMA Baranı A, Malmır F. NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX. Konuralp J. Math. 2016;4:1–22.
MLA Baranı, A. and F. Malmır. “NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 1-22.
Vancouver Baranı A, Malmır F. NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS ON A RECTANGULAR BOX. Konuralp J. Math. 2016;4(1):1-22.
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