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Year 2014, Volume: 2 Issue: 1, 90 - 101, 01.06.2014
https://izlik.org/JA55FX98GX

Abstract

References

  • Alomari, M., Darus, M. and Dragomir, S.S., New inequalities of Simpson’s type for s−convex functions with applications, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 9.
  • Bo-Yan Xi, Rui-Fang Bai and Feng Qi, Hermite–Hadamard type inequalities for the m− and (α, m) −geometrically convex functions, Aequat. Math., Springer Basel AG 2012, DOI 1007/s00010-011-0114-x.
  • C¸ . Yıldız, M. G¨urb¨uz and Ahmet Ocak Akdemir, The Hadamard Type Inequalities for M −Convex Functions, arXiv:1011.1543.
  • Dragomir, S.S., Agarwal, R.P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5 (2000), 533-579. E. Set, M. Sardari, M.E. ¨ Ozdemir and J. Rooin,
  • Hadamard inequality for (α, m)−convex functions, Kyungpook Math. J. 52(2012), 307-317. http://dx.doi.org/10.5666/KMJ.2012.52.3.307.
  • On generalizations of the G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
  • Liu, B.Z., An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
  • M. Emin ¨Ozdemir, Ahmet Ocak Akdemir and Merve Avcı, On Some Hadamard-Type In- equalities for Differentiable m−Convex Functions, arXiv:1112.3866.
  • M.E. ¨Ozdemir, M. Avcı, E. Set, On some inequalities of Hermite–Hadamard type via m−convexity, Appl. Math. Lett. 23 (9) (2010) 1065–1070.
  • M.E. ¨Ozdemir, M. Avcı and H. Kavurmacı, Hermite–Hadamard-type inequalities via (α, m)−convexity, Computers and Mathematics with Applications, 61 (2011), 2614–2620.
  • M.E. ¨Ozdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (α, m)−convex func- tions, Kyungpook Math. J. 50 (2010) 371–378.
  • M.K. Bakula, M. E ¨Ozdemir, J. Peˇcari´c, Hadamard type inequalities for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 9 (2008), Article 96.
  • M. Klariˇci´c Bakula, J. Peˇcari´c, M. Ribiˇci´c, Companion inequalities to Jensen’s inequality for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 7 (2006), Article 194.
  • M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex, RGMIA Res. Rep. Coll. 13 (1) (2010).
  • M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, Some new Hadamard’s type inequalities for co- ordinated m−convex and (α, m)−convex functions, Hacettepe J. of. Math. and Ist., 40, 219- 229, (2011).
  • S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m−convex functions, Tamkang J. Math., 3 (1) 2002.
  • S.S. Dragomir and G.H. Toader, Some inequalities for m−convex functions, Studia Univ. Babe¸s-Bolyai, Math., 38 (1) (1993), 21-28.
  • Ujevi´c, N., Double integral inequalities of Simpson type and applications, J. Appl. Math. and Computing, 14 (2004), no:1-2, p. 213-223.
  • V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
  • Zhongxue, L., On sharp inequalities of Simpson type and Ostrowski type in two independent variables, Comp. and Math. with Appl., 56 (2008), 2043-2047.
  • Van Y¨uz¨unc¨u Yıl University, Faculty of Education, Department of Mathematics Ed- ucation, Van, Turkey E-mail address: havvaonalan@yyu.edu.tr A˘grı ˙Ibrahim C¸ ec¸en University, Faculty of Science and Letters, Department of Mathematics, 04100, A˘grı, Turkey
  • E-mail address: ahmetakdemir@agri.edu.tr Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey E-mail address: erhanset@yahoo.com Department of Mathematics, Faculty of Science and Arts, D¨uzce University, Konu- ralp Campus, D¨uzce, Turkey E-mail address: sarikayamz@gmail.com

SIMPSON'S TYPE INEQUALITIES FOR m-AND (alpha,m)-GEOMETRICALLY CONVEX FUNCTIONS

Year 2014, Volume: 2 Issue: 1, 90 - 101, 01.06.2014
https://izlik.org/JA55FX98GX

Abstract

In this paper, we establish Simpson’s type inequalities for m− and(α, m) −geometrically convex functions using the lemmas

References

  • Alomari, M., Darus, M. and Dragomir, S.S., New inequalities of Simpson’s type for s−convex functions with applications, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 9.
  • Bo-Yan Xi, Rui-Fang Bai and Feng Qi, Hermite–Hadamard type inequalities for the m− and (α, m) −geometrically convex functions, Aequat. Math., Springer Basel AG 2012, DOI 1007/s00010-011-0114-x.
  • C¸ . Yıldız, M. G¨urb¨uz and Ahmet Ocak Akdemir, The Hadamard Type Inequalities for M −Convex Functions, arXiv:1011.1543.
  • Dragomir, S.S., Agarwal, R.P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5 (2000), 533-579. E. Set, M. Sardari, M.E. ¨ Ozdemir and J. Rooin,
  • Hadamard inequality for (α, m)−convex functions, Kyungpook Math. J. 52(2012), 307-317. http://dx.doi.org/10.5666/KMJ.2012.52.3.307.
  • On generalizations of the G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
  • Liu, B.Z., An inequality of Simpson type, Proc. R. Soc. A, 461 (2005), 2155-2158.
  • M. Emin ¨Ozdemir, Ahmet Ocak Akdemir and Merve Avcı, On Some Hadamard-Type In- equalities for Differentiable m−Convex Functions, arXiv:1112.3866.
  • M.E. ¨Ozdemir, M. Avcı, E. Set, On some inequalities of Hermite–Hadamard type via m−convexity, Appl. Math. Lett. 23 (9) (2010) 1065–1070.
  • M.E. ¨Ozdemir, M. Avcı and H. Kavurmacı, Hermite–Hadamard-type inequalities via (α, m)−convexity, Computers and Mathematics with Applications, 61 (2011), 2614–2620.
  • M.E. ¨Ozdemir, H. Kavurmacı, E. Set, Ostrowski’s type inequalities for (α, m)−convex func- tions, Kyungpook Math. J. 50 (2010) 371–378.
  • M.K. Bakula, M. E ¨Ozdemir, J. Peˇcari´c, Hadamard type inequalities for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 9 (2008), Article 96.
  • M. Klariˇci´c Bakula, J. Peˇcari´c, M. Ribiˇci´c, Companion inequalities to Jensen’s inequality for m−convex and (α, m) −convex functions, J. Inequal. Pure Appl. Math. 7 (2006), Article 194.
  • M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex, RGMIA Res. Rep. Coll. 13 (1) (2010).
  • M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, Some new Hadamard’s type inequalities for co- ordinated m−convex and (α, m)−convex functions, Hacettepe J. of. Math. and Ist., 40, 219- 229, (2011).
  • S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m−convex functions, Tamkang J. Math., 3 (1) 2002.
  • S.S. Dragomir and G.H. Toader, Some inequalities for m−convex functions, Studia Univ. Babe¸s-Bolyai, Math., 38 (1) (1993), 21-28.
  • Ujevi´c, N., Double integral inequalities of Simpson type and applications, J. Appl. Math. and Computing, 14 (2004), no:1-2, p. 213-223.
  • V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
  • Zhongxue, L., On sharp inequalities of Simpson type and Ostrowski type in two independent variables, Comp. and Math. with Appl., 56 (2008), 2043-2047.
  • Van Y¨uz¨unc¨u Yıl University, Faculty of Education, Department of Mathematics Ed- ucation, Van, Turkey E-mail address: havvaonalan@yyu.edu.tr A˘grı ˙Ibrahim C¸ ec¸en University, Faculty of Science and Letters, Department of Mathematics, 04100, A˘grı, Turkey
  • E-mail address: ahmetakdemir@agri.edu.tr Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey E-mail address: erhanset@yahoo.com Department of Mathematics, Faculty of Science and Arts, D¨uzce University, Konu- ralp Campus, D¨uzce, Turkey E-mail address: sarikayamz@gmail.com
There are 22 citations in total.

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Authors

HAVVA KAVURMACI Önalan This is me

Ahmet Ocakakdemir This is me

ERHANSET This is me

M.zekisarikaya This is me

Submission Date April 4, 2015
Publication Date June 1, 2014
IZ https://izlik.org/JA55FX98GX
Published in Issue Year 2014 Volume: 2 Issue: 1

Cite

Vancouver 1.HAVVA KAVURMACI Önalan, Ahmet Ocakakdemir, ERHANSET , M.zekisarikaya . SIMPSON’S TYPE INEQUALITIES FOR m-AND (alpha,m)-GEOMETRICALLY CONVEX FUNCTIONS. Konuralp J. Math. [Internet]. 2014 Apr. 1;2(1):90-101. Available from: https://izlik.org/JA55FX98GX
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