Techniques of Integration

Mercer, Peter R.

doi:10.1007/978-1-4939-1926-0_11

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Cited by 2 publications

(2 citation statements)

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“…Remark 1.8. Mercer has applied and employed the double inequality (1.9) in the paper [23] and in the Undergraduate Texts in Mathematics [24].…”

Section: As a Result We Havementioning

confidence: 99%

Refinements of Young's integral inequality via fundamental inequalities and mean value theorems for derivatives

Qi,

Li,

et al. 2020

Preprint

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In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange's and Cauchy's type remainders, and via several fundamental inequalities, such as Čebyšev's integral inequality, Hermite-Hadamard's type integral inequalities, Hölder's integral inequality, and Jensen's discrete and integral inequalities, in terms of higher order derivatives and their norms, survey several applications of several refinements of Young's integral inequality, and further refine Young's integral inequality via Pólya's type integral inequalities.

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“…Remark 1.8. Mercer has applied and employed the double inequality (1.9) in the paper [23] and in the Undergraduate Texts in Mathematics [24].…”

Section: As a Result We Havementioning

confidence: 99%

Refinements of Young's integral inequality via fundamental inequalities and mean value theorems for derivatives

Qi,

Li,

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…We note that Hoorfar-Qi's double inequality (1.2) has been applied and employed in the paper [7] and in the Undergraduate Texts in Mathematics [8].…”

Section: A Concise Retrospectionmentioning

confidence: 99%

Generalizations and applications of Young’s integral inequality by higher order derivatives

Wang

Guo

2019

J Inequal Appl

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In the paper, the authors 1. generalize Young's integral inequality via Taylor's theorems in terms of higher order derivatives and their norms, and 2. apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

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Techniques of Integration

Cited by 2 publications

References 29 publications

Refinements of Young's integral inequality via fundamental inequalities and mean value theorems for derivatives

Refinements of Young's integral inequality via fundamental inequalities and mean value theorems for derivatives

Generalizations and applications of Young’s integral inequality by higher order derivatives

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