Kyungpook Mathematical Journal

  • 제50권3호
  • /
  • Pages.371-378
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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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Ostrowski's Type Inequalities for (α, m)-Convex Function

  • Ozdemir, Muhamet Emin (Ataturk University, K. K. Education Faculty, Department of Mathematics) ;
  • Kavurmaci, Havva (Ataturk University, K. K. Education Faculty, Department of Mathematics) ;
  • Set, Erhan (Ataturk University, K. K. Education Faculty, Department of Mathematics)
  • 투고 : 2010.02.09
  • 심사 : 2010.09.03
  • 발행 : 2010.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

키워드

참고문헌

  1. M. Alomari, M. Darus, S. S. Dragomir and P. Cerone, Ostrowski's inequalities for functions whose derivatives are s-convex in the second sense, RGMIA Res. Rep. Coll., 12(2009), Supplement, Article 15. [ONLINE: http://www.staff.vu.edu.au/RGMIA/v12(E).asp]
  2. M. K. Bakula, M. E. Ozdemir and J. Pecaric, Hadamard type inequalities for m-convex and (${\alpha},\;m$)-convex functions, J. Inequal. Pure & Appl. Math., 9(2008), Article 96, [ONLINE: http://jipam.vu.edu.au].
  3. M. Klaricic Bakula, J. Pecaric, and M. Ribicic, Companion inequalities to Jensen's inequality for m-convex and (${\alpha},\;m$)-convex functions, J. Inequal. Pure & Appl. Math., 7(2006), Article 194, [ONLINE: http://jipam.vu.edu.au].
  4. N. S. Barnett, P. Cerone, S. S. Dragomir, M. R. Pinheiro and A. Sofo, Ostrowski type inequalities for functions whose modulus of derivatives are convex and applications, RGMIA Res. Rep. Coll., 5(2)(2002), Article 1, [ONLINE: http://www.staff.vu.edu.au/RGMIA/v5n2.asp].
  5. S. S. Dragomir, Y. J. Cho and S. S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, J. of Math. Anal. Appl., 245(2)(2000), 489-501. https://doi.org/10.1006/jmaa.2000.6769
  6. S. S. Dragomir and A. Sofo, Ostrowski type inequalities for functions whose derivatives are convex, Proceedings of the 4th International Conference on Modelling and Simulation, November 11-13, 2002, Victoria University, Melbourne, Australia, RGMIA Res. Rep. Coll., 5(2002), Supplement, Article 30, [ONLINE: http://www.staff.vu.edu.au/RGMIA/v5(E).asp].
  7. V. G. Mihesan, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca (Romania) (1993).
  8. E. Set, M. E. Ozdemir and M.Z. Sarikaya, New inequalities of Ostrowski's type for s-convex functions in the second sense with applications, arXiv:1005.0702v1 [math.CA], May 5, 2010.
  9. G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.

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  2. On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-220
  3. Berwald-type inequalities for Sugeno integral with respect to ( α , m , r ) g ${ ( {\alpha,m,r} )_{g}}$ -concave functions vol.2016, pp.1, 2016, https://doi.org/10.1186/s13660-016-0974-7
  4. Hermite–Hadamard type inequality for Sugeno integrals vol.237, 2014, https://doi.org/10.1016/j.amc.2014.03.144
  5. On a New Ostrowski-Type Inequality and Related Results vol.54, pp.4, 2014, https://doi.org/10.5666/KMJ.2014.54.4.545
  6. Hermite–Hadamard-type inequalities for Riemann–Liouville fractional integrals via two kinds of convexity vol.92, pp.11, 2013, https://doi.org/10.1080/00036811.2012.727986
  7. Hermite–Hadamard type integral inequalities for differentiable m-preinvex and (α,m)-preinvex functions vol.23, pp.2, 2015, https://doi.org/10.1016/j.joems.2014.06.006
  8. Hermite–Hadamard-type inequalities via (α,m)-convexity vol.61, pp.9, 2011, https://doi.org/10.1016/j.camwa.2011.02.053
  9. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals vol.63, pp.7, 2012, https://doi.org/10.1016/j.camwa.2011.12.023
  10. Sandor Type Inequalities for Sugeno Integral with respect to Generalα,m,r-Convex Functions vol.2015, 2015, https://doi.org/10.1155/2015/460520
  11. On the generalization of Ostrowski and Grüss type discrete inequalities vol.62, pp.1, 2011, https://doi.org/10.1016/j.camwa.2011.05.026
  12. 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