On inequalities related to some quasi-convex functions
Problemy analiza, Tome 4 (2015) no. 2, pp. 45-64.

Voir la notice de l'article provenant de la source Math-Net.Ru

Estimations of errors in inequalities related to some quasi-convex functions in literature are simplified. Two new general inequalities for functions whose $n$-th derivatives for any positive integer $n$ in absolute values are quasi-convex have been established. Some special cases are discussed with applications in numerical integration and special means.
Keywords: inequalities, quasi-convex function, Simpson type rule, numerical integration, special means.
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Z. Liu. On inequalities related to some quasi-convex functions. Problemy analiza, Tome 4 (2015) no. 2, pp. 45-64. http://geodesic.mathdoc.fr/item/PA_2015_4_2_a4/

[1] Ponstein J., “Seven kinds of convexity”, SIAM Review, 9 (1967), 115–119 | DOI | MR | Zbl

[2] Roberts A. W., Varberg D. E., Convex functions, Academic Press, New York–London, 1973 | MR | Zbl

[3] Alomari M., Darus M., Kirmaci U. S., “Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means”, Computers Math. Applic., 59 (2010), 225–232 | DOI | MR | Zbl

[4] Ion D. A., “Some estimates on the Hermite–Hadamard inequality through quasi-convex functions”, Annals of University of Craiova, Math. Comp. Sci. Ser., 34 (2007), 82–87 | MR

[5] Alomari M., Darus M., Dragomir S. S., “New inequalities of Hermite–Hadamard's type for functions whose second derivatives absolute values are quasi-convex”, Tamkang J. Math., 41:4 (2010), 353–359 | MR | Zbl

[6] Alomari M., Hussain S., “Two inequalities of Simpson type for quasi-convex functions and applications”, Appl. Math. E-Notes, 11 (2011), 110–117 | MR | Zbl

[7] Set E., Özdemir M. E., Sarikaya M. Z., “On new inequalities of Simpson's type for quasi-convex functions with applications”, Tamkang J. Math., 43:3 (2012), 357–364 | DOI | MR | Zbl

[8] Alomari M., Darus M., “On some inequalities of Simpson-type via quasiconvex functions with applicstions”, Transylv. J. Math. Mech., 2:1 (2010), 15–24 | MR

[9] Ardic M. A., Inequalities via $n$-times differentiable quasi-convex functions, 22 Nov 2013, arXiv: 1311.5736v1 [math.CA]

[10] Hussain S., Qaisar S., “New integral inequalities of the type of Hermite–Hadamard through quasi convexity”, Punjab University journal of Mathematics, 45 (2013), 33–38 | MR | Zbl

[11] Hwang D. Y., “Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables”, Appl. Math. Comput., 217 (2011), 9598–9605 | DOI | MR | Zbl

[12] Hwang D. Y., “Some inequalities for differentiable convex mapping with application to weighted midpoint formula and higher moments of random variables”, Appl. Math. Comput., 232 (2014), 68–75 | DOI | MR

[13] Özdemir M. E., Yildiz Ç., Akdemir A. O., “On some new Hadamard-type inequalities for co-ordinated quasi-convex functions”, Hacettepe Journal of Mathematics and Statistics, 41:5, pp (2012), 697–707 | MR | Zbl

[14] Liu Z., “On generalizations of some classical integral inequalities”, J. Math. Inequal., 7:2 (2013), 255–269 | DOI | MR | Zbl