Some inequalities of Hermite-Hadamard type for n--times differentiable (\(\rho, m\))--geometrically convex functions

Volume 8, Issue 3, pp 201--217 http://dx.doi.org/10.22436/jnsa.008.03.04

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1934 Downloads
• 3095 Views

Authors

Fiza Zafar - Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. Humaira Kalsoom - Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. Nawab Hussain - Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia.

Abstract

In this paper, some generalized Hermite-Hadamard type inequalities for n-times differentiable (\(\rho, m\))- geometrically convex function are established. The new inequalities recapture and give new estimates of the previous inequalities for first differentiable functions as special cases. The estimates for trapezoid, midpoint, averaged mid-point trapezoid and Simpson's inequalities can also be obtained for higher differentiable generalized geometrically convex functions.

Share and Cite

Keywords

• Hermite-Hadamard inequality
• (\(\rho، m\))-geometrically convex functions
• n-times differentiable function.

MSC

•  26D15
•  26A15

References

• [1] P. Cerone, S. S. Dragomir, Three point identities and inequalities for n-time differentiable functions, SUT. J., 36 (2000), 351-384.


• [2] S. S. Dragomir, Two mappings in connection to Hadamard's inequality, J. Math. Anal. Appl., 167 (1992), 49-56.


• [3] S. S . Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95.


• [4] S. S. Dragomir, J. E. Pečarić, J. Sándor, A note on the Jensen-Hadamard's inequality, Anal. Num. Ther. Approx., 19 (1990), 29-34.


• [5] M. Masjed-Jamei, N. Hussain, More results on a functional generalization of the Cauchy-Schwarz inequality, J. Inequal. Appl., 2012 (2012), 9 pages.


• [6] P. Montel , Sur les functions convexes et les fonctions sousharmoniques, J. Math. Inequal., 9 (1928), 29-60.


• [7] M. E. Özdemir, C. Yildiz, New Ostrowski type inequalities for geometrically convex functions, Int. J. Mod. Math. Sci., 8 (2013), 27-35.


• [8] Bo-Yan Xi, Rui-Fang Bai, Feng Qi , Hermite-Hadamard type inequalities for the m-and (\(\alpha,m\))-geometrically convex functions, Aequationes Math., 84 (2012), 261-269.


• [9] X. M. Zhang , Geometrically Convex Functions, Anhui University Press(In Chinese). , Hefei (2004)


• [10] X. M. Zhang, Y. M. Chu, The geometrical convexity and concavity of integral for convex and concave functions, Int. J. Mod. Math., 3 (2008), 345-350.


• [11] X. M. Zhang, Z. H. Yang, Differential criterion of n-dimensional geometrically convex functions, J. Appl. Anal., 13 (2007), 197-208.


• [12] X. M. Zhang, An inequality of the Hadamard type for the geometrically convex functions (in Chinese), Math. Pract. Theory, 34 (2004), 171-176.