Random variable inequalities involving (k,s)-integration

M. Houas; Z. Dahmani

doi:10.26637/MJM0504/0005

Abstract

In this paper, we use the (k,s)− Riemann-Liouville operator to establish new results on integral inequalities by using fractional moments of continuous random variables.

Keywords:

(k,s)− Riemann-Liouville integral, random variable, (k,s)− fractional expectation, (k,s)− fractional variance, (k,s)−fractional moment

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

M. Houas Laboratory FIMA, UDBKM, University of Khemis Miliana, Algeria.
Z. Dahmani Laboratory LPAM, UMAB, University of Mostaganem, Algeria.

Pages: 641-646
Date Published: 01-10-2017
Vol. 5 No. 04 (2017): Malaya Journal of Matematik (MJM)

A. Akkurt, Z. Kaçar, H. Yildirim, Generalized fractional integral inequalities for continuous random variables, Journal of Probability and Statistics. Vol 2015. Article ID $958980,(2015), 1-7$.

K. Boukerrioua T. Chiheb and B. Meftah , Fractional hermite hadamard type inequalities for functions whose second derivative are $(s, r)$-convex in the second sense. Kragujevac. J. Math. 40(2) (2016), 72-191.

[.Z. Darhbpani, Fractional integral inequalities for continuous random variables, Malaya J. Math. 2(2), (2014), 172-179.

Z. Dahmani, New applications of fractional calculus on probabilistic random variables. Acta Math. Univ. Come$(3,26)^{text {nianae. } 86(2) ~(2016), ~ 1-9 . ~}$

Z. Dahmani, New classes of integral inequalities of fractional order, Le Matematiche 69(1) (2014), 227-235.

Z. Dahmani, A.E. Bouziane, M. Houas and M. Z. Sarikaya, New $W$-weighted concepts for continuous random variables with applications, Note di Matematica. accepted, (2017).

M. Houas, Certain weighted integral inequalities involving the fractional hypergeometric operators. SCIENTIA, Series A : Mathematical Science. 27 (2016), 87-97.

M. Houas, Some new Saigo fractional integral inequalities in quantum calculus. Facta Universitatis (NIS) Ser. Math. Inform. 31(4) (2016), 761-773.

P. Kumar, Inequalities involving moments of a continuous random variable defined over a finite interval. Computers and Mathematics with Applications, 48, (2004), 257-273.

P. Kumar, The Ostrowski type moment integral inequalities and moment-bounds for continuous random variables. Comput. Math. Appl. 49 (2005), 1929-1940.

V. Lakshmikantham and A. S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Appl. Anal. 11 (2007), no. 3-4, 395-402.

Z. Liu, Some Ostrowski-Gr"uss type inequalities and (3.28) lications. Comput. Math. Appl. 53 (2007), no. 1, $73-$ 79.

S. Mubeen, $k$-Fractional Integrals and Application. Int. J. Contemp. Math. Sciences. 7(2) (2012), 89-94.

M. Z. Sarikaya, Z. Dahmani, M.E. Kiris and F. Ahmad, $(k, s)$-Riemann-Liouville fractional integral and applications.Hacet J.Math.Stat.45(1) (2016), 1-13.

M. 7.29 Sarikaya and A. Karaca, On the $k$-Riemann-Liouville fractional integral and applications. International Journal of Statistics and Mathematics. 1(3) (2014), 033-043.

M. Z. Sarikaya, S. Erden, New weighted integral inequalities for twice differentiable convex functions. Kragujevac. J. Math $40(1)(2016), 15-33$.

M. Tomar, S. Maden, E. Set, $(k, s)$-Riemann-Liouville fractional integral inequalities for continuous random variables. Arab. J. Math. 6 (2017), 55-63.