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2003•Journal of Liaoning Normal UniversityRequires access

On the Equivalence between Some Integral Inequalities

Jing Hao

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Abstract

The inequalities, inequality G(a)≤A(a), cauchy inequality, Tchebychef inequality, Lyapunov inequality, нёlder inequality, triangle inequality and Minkowski inequality,are given and their equivalence are proved.We have proved that they are all equivalent to ∫baτ2(x)dx0.

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The inequalities, inequality G(a)≤A(a), cauchy inequality, Tchebychef inequality, Lyapunov inequality, нёlder inequality, triangle inequality and Minkowski inequality,are given and their equivalence are proved.We have proved that they are all equivalent to ∫baτ2(x)dx0.

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Available abstract

The inequalities, inequality G(a)≤A(a), cauchy inequality, Tchebychef inequality, Lyapunov inequality, нёlder inequality, triangle inequality and Minkowski inequality,are given and their equivalence are proved.We have proved that they are all equivalent to ∫baτ2(x)dx0.

Key concepts: Mathematics, Hölder's inequality, Inequality, Cauchy–Schwarz inequality, Equivalence (formal languages), Kantorovich inequality, Log sum inequality, Rearrangement inequality

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