• Korean Journal of Mathematics
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• 제29권4호
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• pp.687-704
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• 2021

The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly (α, m)-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.845-859
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• 2016

In this paper, some Hermite-Hadamard-$Fej{\acute{e}}r$ type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.169-181
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• 2007

Applying the properties of Hadamard core for totally nonnegative matrices, we give new lower bounds of the determinant for Hadamard product about matrices in Hadamard core and totally nonnegative matrices, the results improve Oppenheim inequality for tridiagonal oscillating matrices obtained by T. L. Markham.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.303-314
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• 2014

In this paper, a new lemma is established and several new inequalities for differentiable co-ordinated quasi-convex functions in two variables which are related to the left-hand side of Hermite-Hadamard type inequality for co-ordinated quasi-convex functions in two variables are obtained.

• 대한수학회논문집
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• 제31권1호
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• pp.53-64
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• 2016

In this paper, we give generalization of the $Fej\acute{e}r$-Hadamard inequality by using definition of convex functions on n-coordinates. Results given in [8, 12] are particular cases of results given here.

• 대한수학회보
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• 제52권3호
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• pp.707-716
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• 2015

Some Hermite-Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11, 12].

• 호남수학학술지
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• 제44권1호
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• pp.17-25
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• 2022

The Hermite-Hadamard integral inequality for F_h-convex functions on time scales is established. The applicability of our results ranges from Optimization problems to Calculus of Variations and to Economics. Application to the Calculus of Variations on time scales is discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.33-48
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• 2024

In this study, we would like to state two refined results related to Hermite Hadamard type inequality for convex functions with two distinct techniques. Hence our obtained results would be better than the results already established for the class of convex functions. Applications to trapezoidal rule and special means are also discussed.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.673-683
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• 2009

We point out: to make Hermtian matrices A and B satisfy Styan matrix inequality, the condition "positive definite property" demanded in the present literatures is not necessary. Furthermore, on the premise of abandoning positive definite property, we derive Styan matrix inequality of Hadamard product for inverse Hermitian matrices and the sufficient and necessary conditions that the equation holds in our paper.

• Korean Journal of Mathematics
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• 제31권1호
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• pp.75-94
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• 2023

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly (s, m)-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.