• 대한수학회지
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• 제39권3호
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• pp.351-361
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• 2002

We extend the Holder-McCarthy inequality for a positive and an arbitrary operator, respectively. The powers of each inequality are given and the improved Reid's inequality by Halmos is generalized. We also give the bound of the Holder-McCarthy inequality by recursion.

• 대한수학회지
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• 제45권3호
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• pp.821-834
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• 2008

Refinements of a variant of Jensen's inequality for functions with nondecreasing increments are presented. Obtained results are used to prove refinements of related variants of Cebysev's inequality and Holder's inequality.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.9-15
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• 2020

In 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse Hölder inequality. We note that many existing inequalities related to the Hölder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].

• Korean Journal of Mathematics
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• 제29권3호
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• pp.467-472
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• 2021

In this paper, we give some new Copson-type integral inequality with a sharp constant.

• 충청수학회지
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• 제35권2호
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• pp.161-170
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• 2022

It is presented a Banach space of functions of bounded mean oscillation BMO type.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.807-811
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• 2022

In this paper, we have proved a general theorem dealing with φ-| C, α, β |_κ summability factors of infinite series. Also, we have obtained some new and known results related to the different special summability methods.

• 호남수학학술지
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• 제44권2호
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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.

• 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.

• 호남수학학술지
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• 제43권3호
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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.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.107-114
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• 2018

We establish some new ostrowski type inequalities for MT-convex function including first order derivative via Niemann-Trouvaille fractional integral. It is interesting to mention that our results provide new estimates on these types of integral inequalities for MT-convex functions.