• East Asian mathematical journal
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• 제21권2호
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• pp.137-150
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• 2005

Bounds for discrete Chebychev functionals that involve means of sequences of different lengths are investigated in the current article. Earlier bounds for the Chebychev functional involving sums of sequences of the same lengths are utilised in the current development. Weighted generalised Chebychev functionals are also examined.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.593-605
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• 2002

Explicit hounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1161-1168
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• 2016

Belarbi and Dahmani [3], recently, using the Riemann-Liouville fractional integral, presented some interesting integral inequalities for the Chebyshev functional in the case of two synchronous functions. Subsequently, Dahmani et al. [5] and Sulaiman [17], provided some fractional integral inequalities. Here, motivated essentially by Belarbi and Dahmani's work [3], we aim at establishing certain (presumably) new inequalities associated with pathway fractional integral operators by using synchronous functions which are involved in the Chebychev functional. Relevant connections of the results presented here with those involving Riemann-Liouville fractional integrals are also pointed out.