Currently displaying 1 – 18 of 18

Showing per page

Order by Relevance | Title | Year of publication

Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

J. MatkowskiT. Świątkowski — 1993

Fundamenta Mathematicae

Let ϕ be an arbitrary bijection of + . We prove that if the two-place function ϕ - 1 [ ϕ ( s ) + ϕ ( t ) ] is subadditive in + 2 then ϕ must be a convex homeomorphism of + . This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of + are also given. We apply the above results to obtain several converses of Minkowski’s inequality.

Some remarks on a problem of C. Alsina.

J. MatkowskiM. Sablik — 1986


Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: [4]...

Uniformly continuous composition operators in the space of functions of two variables of bounded ϕ -variation in the sense of Wiener

J. A. GuerreroJ. MatkowskiN. Merentes — 2010

Commentationes Mathematicae

Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener ϕ -variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable....

Page 1

Download Results (CSV)