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Level sets of continuous functions increasing with respect to each variable

100%

Sajbura K.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2005

tom 25

nr 1

19-26

We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.

On a linear functional equation with a mean-type mapping having no fixed points

100%

Sajbura K.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2005

tom 25

nr 1

27-46

Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.

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2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2 Sajbura K.

2 2005

Wyniki wyszukiwania

Level sets of continuous functions increasing with respect to each variable

On a linear functional equation with a mean-type mapping having no fixed points