• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.305-313
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• 2012

In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.441-452
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• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.701-708
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• 2001

In this article, using the properties of power mean, some new generalizations of the strengthened Hardy's inequalities are given.

• 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.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1021-1026
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• 2001

In this paper, we give an improvement of Carleman’s inequality by using the strict monotonicity of the power mean of n distinct positive numbers.

• 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.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.321-326
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• 2021

In the present paper, a theorem on 𝜑 - | C, 𝛼; 𝛿 |_k summability of an infinite series is obtained by using a quasi 𝛽-power increasing sequence.

• 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.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.161-172
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• 2016

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.