Further generalizations on some hardy type RL-integral inequalities

In this paper, we study generalizations of some integral inequalities related to Hardy type integral inequalities via $(p, q)$ ( p , q ) -calculus. Many results obtained in this paper provide extensions of existing results in the literature. Furthermore, some examples are given to illustrate the investigated results.

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Generalizations of some integral inequalities related to Hardy type integral inequalities via $(p,q)$-calculus

Thongjob

Nonlaopon

Tariboon

et al. 2021

J Inequal Appl

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Reverses Hardy-type inequalities via Jensen integral inequality

Benaissa

Benguessoum

2021

MathMon

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The integral inequalities concerning the inverse Hardy inequalities have been studied by a large number of authors during this century, of these articles have appeared, the work of Sulaiman in 2012, followed by Banyat Sroysang who gave an extension to these inequalities in 2013. In 2020 B. Benaissa presented a generalization of inverse Hardy inequalities. In this article, we establish a new generalization of these inequalities by introducing a weight function and a second parameter. The results will be proved using the Hölder inequality and the Jensen integral inequality. Several the reverses weighted Hardy’s type inequalities and the reverses Hardy’s type inequalities were derived from the main results.

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Discussions on Hardy-type inequalities via Riemann-Liouville fractional integral inequality

Benaissa

2022

MathMon

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In this paper, we have shown that in the article entitled “New Riemann-Liouville generalizations for some inequalities of Hardy type” the Theorem 3.3 is false and that a necessary condition on the order α must be in Theorem 3.1 and Theorem 3.2. Additionally, the correct Theorem 3.3 and a new result with negative parameter are given; these results will prove using the Hölder inequality, and reverse Hölder inequality.

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Further generalizations on some hardy type RL-integral inequalities

Cited by 3 publications

References 13 publications

Generalizations of some integral inequalities related to Hardy type integral inequalities via $(p,q)$-calculus

Generalizations of some integral inequalities related to Hardy type integral inequalities via $(p,q)$-calculus

Reverses Hardy-type inequalities via Jensen integral inequality

Discussions on Hardy-type inequalities via Riemann-Liouville fractional integral inequality

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