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New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications

Yıl 2020, Cilt: 5 Sayı: 3, 290 - 304, 30.12.2020

Öz

In this paper, some new Ostrowski-type inequalities for functions whose derivatives in absolute values are quasi-convex are established. Some applications to special means of real numbers and applications for P.D.F's are given. We also give some applications of our results to get new error bounds for the sum of the midpoint formula.

Kaynakça

  • T-Y. Zhang and F. Qi, Integral inequalities of Hermite–-Hadamard type for m-AH convex functions, Turkish Journal of Analysis and Number Theory, 2014, Vol. 2, No. 3, 60-64
  • M. Alomari, M. Darus and U.S. Kırmacı, Refinements of Hadamard-type inequalities for quasi- convex functions with applications to trapezoidal formula and to special means, Comp. Math. Appl., 59 (2010), 225–232.
  • M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamard’s type for functions whose second derivatives absolute values are quasi-convex, Tamk. J. Math. 41 (2010)353-359.
  • M. Alomari and M. Darus, Some Ostrowski type inequalities for quasi-convex functions with applications to special means, RGMIA, 13 (2) (2010), article No. 3.
  • M. Alomari and M. Darus, On some inequalities Simpson-type via quasi-convex functions with applications, Trans. J. Math. Mech., (2) (2010), 15–24.
  • D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of University of Craiova Math. Comp. Sci. Ser., 34 (2007), 82–87.
  • J.E. Peµcaric, F. Proschan Y.L. and Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
  • A. Ostrowski, Über die Absolutabweichung einer differentierbaren Funktion von ihren Inte-gralmittelwert, Comment. Math. Helv., 10, 226-227, (1938).
Yıl 2020, Cilt: 5 Sayı: 3, 290 - 304, 30.12.2020

Öz

Kaynakça

  • T-Y. Zhang and F. Qi, Integral inequalities of Hermite–-Hadamard type for m-AH convex functions, Turkish Journal of Analysis and Number Theory, 2014, Vol. 2, No. 3, 60-64
  • M. Alomari, M. Darus and U.S. Kırmacı, Refinements of Hadamard-type inequalities for quasi- convex functions with applications to trapezoidal formula and to special means, Comp. Math. Appl., 59 (2010), 225–232.
  • M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamard’s type for functions whose second derivatives absolute values are quasi-convex, Tamk. J. Math. 41 (2010)353-359.
  • M. Alomari and M. Darus, Some Ostrowski type inequalities for quasi-convex functions with applications to special means, RGMIA, 13 (2) (2010), article No. 3.
  • M. Alomari and M. Darus, On some inequalities Simpson-type via quasi-convex functions with applications, Trans. J. Math. Mech., (2) (2010), 15–24.
  • D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of University of Craiova Math. Comp. Sci. Ser., 34 (2007), 82–87.
  • J.E. Peµcaric, F. Proschan Y.L. and Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
  • A. Ostrowski, Über die Absolutabweichung einer differentierbaren Funktion von ihren Inte-gralmittelwert, Comment. Math. Helv., 10, 226-227, (1938).
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume V Issue III 2020
Yazarlar

Alper Ekinci 0000-0003-1589-2593

Muhamet Emin Özdemir 0000-0002-5992-094X

Erhan Set 0000-0003-1364-5396

Yayımlanma Tarihi 30 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 5 Sayı: 3

Kaynak Göster

APA Ekinci, A., Özdemir, M. E., & Set, E. (2020). New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. Turkish Journal of Science, 5(3), 290-304.
AMA Ekinci A, Özdemir ME, Set E. New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. TJOS. Aralık 2020;5(3):290-304.
Chicago Ekinci, Alper, Muhamet Emin Özdemir, ve Erhan Set. “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions With Applications”. Turkish Journal of Science 5, sy. 3 (Aralık 2020): 290-304.
EndNote Ekinci A, Özdemir ME, Set E (01 Aralık 2020) New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. Turkish Journal of Science 5 3 290–304.
IEEE A. Ekinci, M. E. Özdemir, ve E. Set, “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications”, TJOS, c. 5, sy. 3, ss. 290–304, 2020.
ISNAD Ekinci, Alper vd. “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions With Applications”. Turkish Journal of Science 5/3 (Aralık 2020), 290-304.
JAMA Ekinci A, Özdemir ME, Set E. New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. TJOS. 2020;5:290–304.
MLA Ekinci, Alper vd. “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions With Applications”. Turkish Journal of Science, c. 5, sy. 3, 2020, ss. 290-04.
Vancouver Ekinci A, Özdemir ME, Set E. New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. TJOS. 2020;5(3):290-304.