On inequalities of Hermite-Hadamard type for stochastic processes whose third derivative absolute values are quasi-convex

Main Article Content

Jesus Enrique Materano
Nelson Merentes
Maira Lopez-Valera

Abstract

In this paper we give some estimates of the right-hand side inequality of Hermite-Hadamad type for stochastic processes whose third derivatives in absolute values are quasi-convex.

Article Details

How to Cite
Materano, J. E., Merentes, N., & Lopez-Valera, M. (2017). On inequalities of Hermite-Hadamard type for stochastic processes whose third derivative absolute values are quasi-convex. Tamkang Journal of Mathematics, 48(2), 203–208. https://doi.org/10.5556/j.tkjm.48.2017.2359
Section
Papers
Author Biographies

Jesus Enrique Materano

Escuela de Matemática, Universidad Central de Venezuela, Caracas 1220A-Venezuela.

Nelson Merentes

Escuela de Matemática, Universidad Central de Venezuela, Caracas 1220A-Venezuela

Maira Lopez-Valera

Escuela deMatemática, Universidad Central de Venezuela, Caracas 1220A-Venezuela

References

M. Alomari, Several inequalities of Hermite-Hadamard, Ostrowski and Simpson type for $s$-convex, quasi-convex and $r$-convex mappings and applications, Faculty of Science and Technology, Universiti Kebangssan Malaysia, Bangi, 2008.

M. Alomari, M. Darus, S. S. Dragomir, Ner inequalities of Hermite-Hadamard type for functions whose second derivatives absolute value are quasi-convex, Tamkang Journal on Mathematics, 41(2010), 353--359.

D. Barraez, L. Gonzalez, N. Merentes, A. M. Moros, On $h$-convex stochastic process, Mathematica Aeterna, 5(2015),571--581.

S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Applied Mathematics Letters, 11(1998),91--95.

L. Fejer, Uber die Fourierreihen, II Math. Naturwiss, Anz. Ungar, Akad. Wiss., 24(1906), 369--390.

L. Gonzalez, N. Merentes, M. Valera-Lopez, Some estimates on the Hermite-Hadamard inequality through convex and quasi-convex stochastic processes, Mathematica Aeterna, 5(2015), 745--767.

D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex function, Annals of University of Craiova Math. Comp., 147(2004), 137--146.

U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Applied Mathematics and Computation, 147(2004), 137--146.

B. Nagy, On a generalization of the Cauchy equation, Aequationes Math., 10(1974), 165--171.

K. Nikodem, On convex stochastic processes}, Aequationes Math., 20(1980), 184--197.

K. Nikodem, On quadratic stochastic processes, Aequationes Math., 21(1980), 192--99.

C. E. M. Pearce and J. Pevcaric, Inequalities for differentiable mappinggs with application to special means and quadrature formula. Applied Mathematics Letter, 13(2000), 51--55.

P. Niculescu and L. E. Persson, Convex functions and their applications,A comtemporary approach CMS Books in Mathematics, 23, Springer-Verlag, New York, 2006.

S. Qaisar, S. Hussain and Ch. He, On new inequalities of Hermite-Hadamard type for functions whose thrid derivative absolute values are quasi-convex with applications, Journal of the Egyptian Mathematical Society, 2(2014), 19--22.

K. Sobczyk, Stochastic differential equations with applications to physics and engineering, Kluwer Academic Publishers B. V. (1991).

M. Z. Sarikaya, E. Set and M. E. Ozdemir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex, arXiv:1005.0451v1. (2010).