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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).

Ayrıntılar

Birincil Dil İngilizce
Konular Fen
Bölüm Volume V Issue III 2020
Yazarlar

Alper EKİNCİ (Sorumlu Yazar)
BANDIRMA ONYEDI EYLUL UNIVERSITY
0000-0003-1589-2593
Türkiye


Muhamet Emin ÖZDEMİR
ULUDAG UNIVERSITY
0000-0002-5992-094X
Türkiye


Erhan SET
ORDU UNIVERSITY
0000-0003-1364-5396
Türkiye

Yayımlanma Tarihi 30 Aralık 2020
Yayınlandığı Sayı Yıl 2020, Cilt 5, Sayı 3

Kaynak Göster

Bibtex @araştırma makalesi { tjos834903, journal = {Turkish Journal of Science}, issn = {2587-0971}, eissn = {2587-0971}, address = {KED YAYINCILIK LTD. ŞTİ. Ağrı}, publisher = {Ahmet Ocak AKDEMİR}, year = {2020}, volume = {5}, number = {3}, pages = {290 - 304}, title = {New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications}, key = {cite}, author = {Ekinci, Alper and Özdemir, Muhamet Emin and Set, Erhan} }
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 . Retrieved from https://dergipark.org.tr/tr/pub/tjos/issue/59057/834903
MLA Ekinci, A. , Özdemir, M. E. , Set, E. "New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications" . Turkish Journal of Science 5 (2020 ): 290-304 <https://dergipark.org.tr/tr/pub/tjos/issue/59057/834903>
Chicago Ekinci, A. , Özdemir, M. E. , Set, E. "New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications". Turkish Journal of Science 5 (2020 ): 290-304
RIS TY - JOUR T1 - New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications AU - Alper Ekinci , Muhamet Emin Özdemir , Erhan Set Y1 - 2020 PY - 2020 N1 - DO - T2 - Turkish Journal of Science JF - Journal JO - JOR SP - 290 EP - 304 VL - 5 IS - 3 SN - 2587-0971-2587-0971 M3 - UR - Y2 - 2020 ER -
EndNote %0 Turkish Journal of Science New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications %A Alper Ekinci , Muhamet Emin Özdemir , Erhan Set %T New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications %D 2020 %J Turkish Journal of Science %P 2587-0971-2587-0971 %V 5 %N 3 %R %U
ISNAD Ekinci, Alper , Özdemir, Muhamet Emin , Set, Erhan . "New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications". Turkish Journal of Science 5 / 3 (Aralık 2020): 290-304 .
AMA Ekinci A. , Özdemir M. E. , Set E. New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. TJOS. 2020; 5(3): 290-304.
Vancouver Ekinci A. , Özdemir M. E. , Set E. New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications. Turkish Journal of Science. 2020; 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", Turkish Journal of Science, c. 5, sayı. 3, ss. 290-304, Ara. 2020