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HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

  • A. BARANI (a1) and S. BARANI (a2)
Abstract
Abstract

In this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

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Copyright
Corresponding author
For correspondence; e-mail: alibarani2000@yahoo.com
References
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[1]Akdemir A. O. and Özdemir M. E., ‘Some Hadamard-type inequalities for coordinated P-convex functions and Godunova–Levin functions’, AIP Conf. Proc. 1309 (2010), 7–15.
[2]Barani A., Ghazanfari A. G. and Dragomir S. S., ‘Hermite–Hadamard inequality through prequasiinvex functions’, RGMIA Res. Rep. Coll. 14 (2011), article 48.
[3]Barani A., Barani S. and Dragomir S. S., ‘Refinements of Hermite–Hadamard type inequality for functions whose second derivatives absolute values are quasiconvex’, RGMIA Res. Rep. Coll. 14 (2011), article 69.
[4]Dragomir S. S., ‘Two mappings on connection to Hadamard’s inequality’, J. Math. Anal. Appl. 167 (1992), 4956.
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[8]Dragomir S. S. and Pearce C. E. M., ‘Quasiconvex functions and Hadamard’s inequality’, Bull. Aust. Math. Soc. 57 (1998), 377385.
[9]Dragomir S. S. and Agarwal R. P., ‘Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula’, Appl. Math. Lett. 11 (1998), 9195.
[10]Ion D. A., ‘Some estimates on the Hermite–Hadamard inequality through quasiconvex functions’, Ann. Univ. Craiova Math. Comp. Sci. Ser. 34 (2007), 8287.
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[13]Tseng K. L., Yang G. S. and Dragomir S. S., ‘On quasiconvex functions and Hadamard’s inequality’, RGMIA Res. Rep. Coll. 14 (2003), article 1.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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