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Weighted extended mean values

Alfred Witkowski (2004)

Colloquium Mathematicae

The author generalizes Stolarsky's Extended Mean Values to a four-parameter family of means F(r,s;a,b;x,y) = E(r,s;ax,by)/E(r,s;a,b) and investigates their monotonicity properties.

Weighted Hardy's inequalities for negative indices.

Dmitryi V. Prokhorov (2004)

Publicacions Matemàtiques

In the paper we obtain a precise characterization of Hardy type inequalities with weights for the negative indices and the indices between 0 and 1 and establish a duality between these cases.

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 inequalities for monotone functions.

L. Maligranda (1997)

Collectanea Mathematica

We give characterizations of weights for which reverse inequalities of the Hölder type for monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement previous results.

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 ≥ 0 and nonnegative weights u and v and N ≥ 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.

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