• 호남수학학술지
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• 제45권1호
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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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• 제9권1호
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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.

• 대한수학회보
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• 제42권2호
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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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• 제13권1_2호
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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.

• 대한수학회보
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• 제49권4호
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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.

• 호남수학학술지
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• 제48권1호
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• pp.87-108
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• 2026

In this paper we first recall the concepts (q - h)-derivatives and (q - h)-integrals. Moreover, we present several properties of these concepts. Then, we prove a new version of Hermite-Hadamard inequality including (q - h)-integrals. Furthermore, we establish two new identities for (q - h)-differentiable functions. Then, by these equalities, we prove several midpoint and trapezoid type inequalities. We also present the relation the results proved in this paper and the earlier ones. Finally, we validate these inequalities with examples of convex functions showing their accuracy and applicability.

• 한국수학교육학회지시리즈B:이론수학과 교직수학
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• 제31권3호
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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.