2013
DOI: 10.7153/jmi-07-22
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Chebyshev type inequalities for the Saigo fractional integrals and their q-analogues

Abstract: 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.Mathematics subject classification (2010): 26D10, 26A33, 05A30.

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Cited by 37 publications
(43 citation statements)
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“…The results given earlier by Purohit and Raina (2013) and Dahmani et al (2011) are special cases of results obtained in present paper. …”
mentioning
confidence: 57%
“…The results given earlier by Purohit and Raina (2013) and Dahmani et al (2011) are special cases of results obtained in present paper. …”
mentioning
confidence: 57%
“…Therefore, several generalizations of this type of integral inequality have been extensively addressed by researchers (see, e.g., [16], [20], [21], [22], [25], [26], [29], [34], [35], [36], [39], [40], [41], [49]). Moreover, by applying fractional integral operators and fractional q-integral operators, many authors have obtained a lot of fractional integral inequalities, their q-analogues and applications (see, e.g., [7], [11], [12], [13], [14], [17], [28], [38], [42], [43], [51], and the references cited therein).…”
Section: Introductionmentioning
confidence: 99%
“…There is a large number of the fractional integral operators discussed in the literature, but because of their applications in many fields of sciences, the Riemann-Liouville and Hadamard fractional integral operators have been studied extensively [7,8,11,15,16,21,29,31]. Further, for inequalities involving generalized fractional operators one can see [4][5][6][24][25][26][27][28].…”
Section: Introductionmentioning
confidence: 99%