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CHEBYSHEV TYPE INEQUALITIES FOR THE SAIGO FRACTIONAL INTEGRALS AND THEIR q–ANALOGUES

Journal of Mathematical Inequalities (Impact Factor: 0.63). 01/2013; 7(2):239–249.

ABSTRACT

The aim of the present paper is to obtain certain new integral inequalities involving the Saigo fractional integral operator. It is also shown how the various inequalities considered in this paper admit themselves of q-extensions which are capable of yielding various results in the theory of q-integral inequalities.

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Available from: Sunil Dutt Purohit
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    • "whereíµí±“,íµí±”aretwodifferentiablefunctionsandíµí±“ í®í° ∈íµí°¿íµí±Ÿ(íµí±Ž,íµí±), íµí±” í®í° ∈íµí°¿íµí±(íµí±Ž,íµí±),íµí±Ÿ>1,íµí±Ÿ −1 +íµí± −1 =1.Recently, Dahmanietal.[28]establishedsomeintegralresultsrelated toChebyshev'sfunctional(3)inthecaseofdifferentiable functionswhosederivativesbelongtothespaceíµí°¿íµí±([0,∞)), involvingRiemann-Liouvillefractionalintegrals.Purohitand Raina[22] [29]addedonemoredimensiontothisstudyby introducingcertainnewintegralinequalitiesforsynchronous functions,involvingtheSaigofractionalintegraloperators [30].Further,Baleanuetal.[24]establishedcertaingeneral- izedintegralinequalitiesforsynchronousfunctionsthatare relatedtotheChebyshevfunctional(1)usingthefractional hypergeometricoperator,introducedbyCurielandGalué [31]. "
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    ABSTRACT: By making use of the fractional hypergeometric operators, we establish certain new fractional integral inequalities for synchronous functions which are related to the weighted version of the Chebyshev functional. Some consequent results and special cases of the main results are also pointed out.
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    ABSTRACT: Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.
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