An equivalent form of young's inequality with upper bound

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An Equivalent Form of Young’s Inequality with Upper Bound

β1 ψ dx− ab+ α1β1. Young’s inequality [2, 1, 4] states that for every a ∈ [α1, α2] and b ∈ [β1, β2] (2) 0 ≤ F (a, b), where the equality holds iff φ(a) = b (or, equivalently, ψ(b) = a). Among the classical inequalities Young’s inequality is probably the most intuitive. Indeed, its meaning can be easily grasped once the integrals are regarded as areas below and on the left of the graph of φ (see...

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ژورنال

عنوان ژورنال: Applicable Analysis and Discrete Mathematics

سال: 2008

ISSN: 1452-8630,2406-100X

DOI: 10.2298/aadm0802213m