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Dergiler / Turkish Journal of Science / 2020 / Cilt: 5 Sayı: 3

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

Alper Ekinci(BANDIRMA ONYEDI EYLUL UNIVERSITY)0000-0003-1589-2593
Muhamet Emin Özdemir(ULUDAG UNIVERSITY)0000-0002-5992-094X
Erhan Set(ORDU UNIVERSITY)0000-0003-1364-5396
Sayfa
290–304
Yayın Tarihi
2020-12-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also give some applications of our results to get new error bounds for the sum of the midpoint formula.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, some new Ostrowski-type inequalities for functions whose derivatives in absolute values are quasi-convex are established.
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Temel Bulgular & Veri:Some applications to special means of real numbers and applications for P.D.F's are given.
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Sonuç & Katkı:We also give some applications of our results to get new error bounds for the sum of the midpoint formula.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ostrowski inequality · quasi-convex functions · Hölder inequality

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.

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Bu Makaleye Atıf Yap

Ekinci, A., Özdemir, M. E., Set, E. (2020). New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. Turkish Journal of Science, Cilt: 5 Sayı: 3, 290–304. https://ajindex.com/articles/1557559

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Kaynakça (8)

  1. 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
  2. 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.
  3. 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.
  4. 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.
  5. M. Alomari and M. Darus, On some inequalities Simpson-type via quasi-convex functions with applications, Trans. J. Math. Mech., (2) (2010), 15–24.
  6. 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.
  7. J.E. Peµcaric, F. Proschan Y.L. and Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
  8. A. Ostrowski, Über die Absolutabweichung einer differentierbaren Funktion von ihren Inte-gralmittelwert, Comment. Math. Helv., 10, 226-227, (1938).