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The Young inequality and the Δ₂-condition

Philippe Laurençot (2002)

Colloquium Mathematicae

If φ: [0,∞) → [0,∞) is a convex function with φ(0) = 0 and conjugate function φ*, the inequality x y ε φ ( x ) + C ε φ * ( y ) is shown to hold true for every ε ∈ (0,∞) if and only if φ* satisfies the Δ₂-condition.

Weighted inequalities for monotone and concave functions

Hans Heinig, Lech Maligranda (1995)

Studia Mathematica

Characterizations of weight functions are given for which integral inequalities of monotone and concave functions are satisfied. The constants in these inequalities are sharp and in the case of concave functions, constitute weighted forms of Favard-Berwald inequalities on finite and infinite intervals. Related inequalities, some of Hardy type, are also given.

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