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

Year 2020, Volume: 5 Issue: 3, 290 - 304, 30.12.2020

Alper Ekinci Muhamet Emin Özdemir Erhan Set

Abstract

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.

Keywords

Ostrowski inequality quasi-convex functions Hölder inequality Power- mean inequality midpoint formula

References

  • 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).

Year 2020, Volume: 5 Issue: 3, 290 - 304, 30.12.2020

Alper Ekinci Muhamet Emin Özdemir Erhan Set

Abstract

References

  • 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).
There are 8 citations in total.

Details

Primary Language English
Journal Section Volume V Issue III 2020
Authors

Alper Ekinci 0000-0003-1589-2593

Muhamet Emin Özdemir 0000-0002-5992-094X

Erhan Set 0000-0003-1364-5396

Publication Date December 30, 2020
Published in Issue Year 2020 Volume: 5 Issue: 3

Cite

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. December 2020;5(3):290-304.
Chicago Ekinci, Alper, Muhamet Emin Özdemir, and Erhan Set. “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions With Applications”. Turkish Journal of Science 5, no. 3 (December 2020): 290-304.
EndNote Ekinci A, Özdemir ME, Set E (December 1, 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, and E. Set, “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications”, TJOS, vol. 5, no. 3, pp. 290–304, 2020.
ISNAD Ekinci, Alper et al. “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions With Applications”. Turkish Journal of Science 5/3 (December 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 et al. “New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions With Applications”. Turkish Journal of Science, vol. 5, no. 3, 2020, pp. 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.
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