New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications
Yıl 2020,
Cilt: 5 Sayı: 3, 290 - 304, 30.12.2020
Alper Ekinci
,
Muhamet Emin Özdemir
,
Erhan Set
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), 225232.
- M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamards 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), 1524.
- 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), 8287.
- 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
Alper Ekinci
,
Muhamet Emin Özdemir
,
Erhan Set
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), 225232.
- M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamards 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), 1524.
- 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), 8287.
- 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).