• Kyungpook Mathematical Journal
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• v.56 no.3
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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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• v.32 no.3_4
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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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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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].

• Honam Mathematical Journal
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• v.44 no.1
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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.

• The Pure and Applied Mathematics
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• v.31 no.1
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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.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.399-410
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• 2010

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.119-125
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• 2015

In this note, two new mappings associated with convexity are propoesd, by which we obtain some new Hermite-Hadamard type inequalities for convex functions via Riemann-Liouville fractional integrals. We conclude that the results obtained in this work are the refinements of the earlier results.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.709-729
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• 2002

Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established. Some numerical experiments are performed as well.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.301-318
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• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.244-258
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• 2022

In this work, by using an integral identity together with both the Hölder and the power-mean integral inequalities we establish several new inequalities for n-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. In special cases, the results obtained coincide with the well-known results in the literature.