• Honam Mathematical Journal
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• v.45 no.1
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.45-60
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• 2002

Some error estimates in terms of the p-norms of the fourth derivative for the remainder in a perturbed trapezoid formula are given. Applications for the expectation of a random variable and the Hermite-Hadamard divergence in Information Theory are also pointed out.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.213-230
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• 2005

Companions of Ostrowski's integral inequality for absolutely continuous functions and applications for composite quadrature rules and for p.d.J.'s are provided.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.67-84
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• 2003

A quadrature rule for the finite Hilbert Trasnform via trapezoid type inequalities is obtained . Some numerical experiments for different divisions of the interval [a, b] are also presented.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.775-785
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• 2012

Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.

• The Pure and Applied Mathematics
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• v.31 no.3
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• pp.311-324
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• 2024

This article presents the above and below bounds for Midpoint and Trapezoid types inequalities for 𝜓-Hilfer fractional integrals with the assistance of the functions whose second derivatives are bounded. We also possess some extensions and generalizations of Hermite-Hadamard inequalities via 𝜓-Hilfer fractional integrals with the aid of the functions that have the conditions that will said.