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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.

Weighted multidimensional inequalities for monotone functions

Sorina Barza, Lars-Erik Persson (1999)

Mathematica Bohemica

We discuss the characterization of the inequality (RN+ fq u)1/q C (RN+ fp v )1/p, 0<q, p <, for monotone functions $f \geq 0$ and nonnegative weights $u$ and $v$ and $N \geq 1$ . We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.

Weighted norm inequalities for averaging operators of monotone functions.

Christoph J. Neugebauer (1991)

Publicacions Matemàtiques

We prove weighted norm inequalities for the averaging operator Af(x) = 1/x ∫0x f of monotone functions.

Displaying 1 – 3 of 3

Weighted inequalities for monotone and concave functions

Weighted multidimensional inequalities for monotone functions

Weighted norm inequalities for averaging operators of monotone functions.

Currently displaying 1 – 3 of 3