Kyungpook Mathematical Journal

  • 제50권3호
  • /
  • Pages.399-410
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  • 2010
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some New Inequalities of Hermite-Hadamard's Type

  • Saglam, Aziz (Department of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University) ;
  • Yildirim, Huseyin (Department of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University) ;
  • Sarikaya, Mehmet Zeki (Department of Mathematics, Faculty of Science and Arts, Duzce University)
  • 투고 : 2010.02.02
  • 심사 : 2010.07.16
  • 발행 : 2010.09.30
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초록

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

키워드

참고문헌

  1. S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 11(5)(1998), 91-95. https://doi.org/10.1016/S0893-9659(98)00086-X
  2. J. L. W. V. Jensen, On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B., 16, 49-69, 1905.
  3. C. E. M. Pearce and J. Pecaric, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13(2)(2000), 51-55. https://doi.org/10.1016/S0893-9659(99)00164-0
  4. U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147(2004), 137-146. https://doi.org/10.1016/S0096-3003(02)00657-4
  5. U. S. Kirmaci and M. E. Ozdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp., 153(2004), 361-368. https://doi.org/10.1016/S0096-3003(03)00637-4
  6. J. Pecaric, F. Proschan and Y. L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.

피인용 문헌

  1. Some weighted integral inequalities for differentiable preinvex and prequasiinvex functions with applications vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-575
  2. On Generalizations of the Hadamard Inequality for (α, m)-Convex Functions vol.52, pp.3, 2012, https://doi.org/10.5666/KMJ.2012.52.3.307
  3. Some weighted integral inequalities for differentiable h-preinvex functions vol.25, pp.3, 2018, https://doi.org/10.1515/gmj-2016-0081