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THE HADAMARD TYPE INEQUALITIES FOR m−CONVEX FUNCTIONS

Year 2013, Volume: 1 Issue: 1, 40 - 47, 01.06.2013
https://izlik.org/JA52AD94WZ

Abstract

In this paper, we obtained some new Hadamard-Type inequalitiesfor functions whose derivatives absolute values are m−convex. Some applications to special means of real numbers are given

References

  • H. Kavurmacı, M. Avcı, M.E. ¨Ozdemir, New inequalities of Hermite-Hadamard’s type for convex functions with applications, Journal of Inequalities and Applications, 2011, 2011:86.
  • G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
  • S.S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J.Math. Anal. Appl., 167(1992), 49-56.
  • U.S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comp. 147(2004), 137-146.
  • G.S. Yong, D.Y. Hwang and K.L. Tseng, Some inequalitiesfor differentiable convex and concave mappings, Comp. Math. Appl., 47(2004), 207-216.
  • M.K. Bakula, M.E. ¨Ozdemir and J. Pe´cari´c, Hadamard type inequalities for m−convex and (α, m)-convex functions, J. Inequal. Pure and Appl. Math., 9(4) (2008), Article 96.
  • S.S. Dragomir and G. Toader, Some inequalities for m−convex functions, Studia Univ. Babes- bolyai. Mathematica, 38(1993), 1, 21-28.
  • S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Type In- equalities and Applications, RGMIA Monographs, Victoria University, 2000. [ONLINE : http://ajmaa.org/RGMIA/monographs/hermite hadamard.html].
  • ATAT ¨URK UNIVERSITY, K. K. EDUCATION FACULTY, DEPARTMENT OF MATH
  • EMATICS,25240, CAMPUS, ERZURUM, TURKEY E-mail address: yildizc@atauni.edu.tr GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES, A ˘GRI ˙IBRAH˙IM
  • C¸ EC¸ EN UNIVERSITY, A ˘GRI, TURKEY E-mail address: mgurbuz@agri.edu.tr A ˘GRI ˙IBRAH˙IM C¸ EC¸ EN UN˙IVERSITY, FACULTY OF SCIENCE AND ARTS, DE
  • PARTMENT OF MATHEMATICS, 04100, CAMPUS, A ˘GRI, TURKEY E-mail address: ahmetakdemir@agri.edu.tr

Year 2013, Volume: 1 Issue: 1, 40 - 47, 01.06.2013
https://izlik.org/JA52AD94WZ

Abstract

References

  • H. Kavurmacı, M. Avcı, M.E. ¨Ozdemir, New inequalities of Hermite-Hadamard’s type for convex functions with applications, Journal of Inequalities and Applications, 2011, 2011:86.
  • G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Ap- proximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
  • S.S. Dragomir, Two mappings in connection to Hadamard’s inequalities, J.Math. Anal. Appl., 167(1992), 49-56.
  • U.S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comp. 147(2004), 137-146.
  • G.S. Yong, D.Y. Hwang and K.L. Tseng, Some inequalitiesfor differentiable convex and concave mappings, Comp. Math. Appl., 47(2004), 207-216.
  • M.K. Bakula, M.E. ¨Ozdemir and J. Pe´cari´c, Hadamard type inequalities for m−convex and (α, m)-convex functions, J. Inequal. Pure and Appl. Math., 9(4) (2008), Article 96.
  • S.S. Dragomir and G. Toader, Some inequalities for m−convex functions, Studia Univ. Babes- bolyai. Mathematica, 38(1993), 1, 21-28.
  • S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Type In- equalities and Applications, RGMIA Monographs, Victoria University, 2000. [ONLINE : http://ajmaa.org/RGMIA/monographs/hermite hadamard.html].
  • ATAT ¨URK UNIVERSITY, K. K. EDUCATION FACULTY, DEPARTMENT OF MATH
  • EMATICS,25240, CAMPUS, ERZURUM, TURKEY E-mail address: yildizc@atauni.edu.tr GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES, A ˘GRI ˙IBRAH˙IM
  • C¸ EC¸ EN UNIVERSITY, A ˘GRI, TURKEY E-mail address: mgurbuz@agri.edu.tr A ˘GRI ˙IBRAH˙IM C¸ EC¸ EN UN˙IVERSITY, FACULTY OF SCIENCE AND ARTS, DE
  • PARTMENT OF MATHEMATICS, 04100, CAMPUS, A ˘GRI, TURKEY E-mail address: ahmetakdemir@agri.edu.tr
There are 12 citations in total.

Details

Authors

Çetin Yıldız This is me

MustafaGürbüz This is me

Ahmet Ocakakdemir This is me

Submission Date April 4, 2015
Publication Date June 1, 2013
IZ https://izlik.org/JA52AD94WZ
Published in Issue Year 2013 Volume: 1 Issue: 1

Cite

Vancouver 1.Çetin Yıldız, MustafaGürbüz , Ahmet Ocakakdemir. THE HADAMARD TYPE INEQUALITIES FOR m−CONVEX FUNCTIONS. Konuralp J. Math. [Internet]. 2013 Apr. 1;1(1):40-7. Available from: https://izlik.org/JA52AD94WZ
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