New classes of fractional integral inequalities and some recent results on random variables
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DOI:
https://doi.org/10.26637/MJM0803/0002Abstract
In this paper, some applications of Continuous Uniform and Beta probability distributions are developed. Then, by means of Chebyshev and Hölder inequalities, some new results on integral inequalities are established. Finally, some concepts on $\omega$-weighted continuous random variables are further considered to derive some more results.
Keywords:
Fractional integral inequalities, Riemann-Liouville integral, random variable, normalized fractional moment, normalized fractional $omega$ -weighted expectationMathematics Subject Classification:
Mathematics- Pages: 738-743
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
R. P. Agawal, N. Elezovic, J. Pecaric, On some inequalities for Beta and Gamma functions via some classical inequalities. J. Inequal. and Appl., 5(2005), 593-613.
M. Bezziou, Z. Dahmani, Random Inequalities via Riemann-Liouville fractional integration, Under View, 2019.
T. Caccoulos, V. Papathanasiou, On upper bounds for the variance of functions of random variables, Stat. Proba. Lett., 3(1985), 175-184.
T. Caccoulos, V. Papathanasiou, Caracterizations of distribution by variance bounds, Stat. Proba. Lett., 7(1989), $351-356$.
T. Caccoulos, V. Papathanasiou, Characterizations of distributions by generalizations of variance bounds and simple proofs of the CLT, Journal of Statistical Planningand and Inference, 63(1997), 157-171.
Z. Dahmani, tAbout some integral inequalities using Riemann-Liouville integrals, General Mathematics, 20(4)(2012), 63-69.
Z. Dahmani, New applications of fractional calculus on probabilistic random variables, Acta Math. Univ. ComenianaeVol. LXXXVI, 2 (2017), 299-307.
Z. Dahmani, New identities and lower bounds for CUD and Beta distributions, Romai J., 15(1)(2019), 25-35.
Z. Dahmani, New inequalities in fractional integrals, International Journal of Nonlinear Sciences, 9(4)(2010), 493-497.
Z. Dahmani, A.E. Bouziane, M. Houas, M.Z. Sarikaya, New w-weighted concepts for continuous random variables with applications, Note Di Math., 37(1)(2017), $23-40$.
M. DoubbiBounoua, Z. Dahmani, Z. Bekkouche, Further results and applications on continuous random variables, Malaya Journal of Matematik, 7(3)(2019), 429-435.
S.S. Dragomir, R.P. Agarwal, N.S. Barnett, Inequalities for Beta and Gamma functions via some classical and new integral inequalities, J. of lnequal. and Appl., 5(2000), $103-165$.
S.S. Dragomir, P. Kumar, S.P. Singh, Mathematical inequalities with applications to the Beta and Gamma mappings, Indian Jour. Math., 42(3)(2000), 1-19.
F. Goodarzi, M. Amini, G.R. MohtashamiBorzadaran, On upper bounds for the variance of functions of randomvariables with weighted distributions, Labachevskii Journal of Mathematics, 37(4)(2016), 422-435.
R. Gorenflo, F. Mainardi, Fractional Calculus: Integral and Diferential Equations of Fractional Order, Springer Verlag, Wien, (1997), 223-276.
P. Kumar, Inequality involving moments of a continuous random variable defined over a finite interval, Computers and Mathematics with Applications, 48(2004), 257-273.
P. Kumar, S.P. Singh, S.S. Dragomir, Some inequalities involving Beta and Gamma functions, Nonlinear Analysis Forum, 6(1)(2001), 143-150.
I.Sliman, Z. Dahmani: Normalized fractional inequalities for continous random variables. Under View, 2019.
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