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

100%
Sajbura K.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2005
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tom 25
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nr 1
27-46
EN
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.
2
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X-minimal patterns and a generalization of Sharkovskiĭ's theorem

86%
Bobok J., Kuchta M.
Fundamenta Mathematicae
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1998
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tom 156
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nr 1
33-66
EN
We study the law of coexistence of different types of cycles for a continuous map of the interval. For this we introduce the notion of eccentricity of a pattern and characterize those patterns with a given eccentricity that are simplest from the point of view of the forcing relation. We call these patterns X-minimal. We obtain a generalization of Sharkovskiĭ's Theorem where the notion of period is replaced by the notion of eccentricity.
3
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Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

86%
Matkowski J., Świątkowski T.
Fundamenta Mathematicae
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1993
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tom 143
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nr 1
75-85
EN
Let ϕ be an arbitrary bijection of $ℝ_+$. We prove that if the two-place function $ϕ^{-1}[ϕ (s)+ϕ (t)]$ is subadditive in $ℝ^2_+$ then $ϕ $ must be a convex homeomorphism of $ℝ_+$. This is a partial converse of Mulholland's inequality. Some new properties of subadditive bijections of $ℝ_+$ are also given. We apply the above results to obtain several converses of Minkowski's inequality.
4
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K3M: a universal algorithm for image skeletonization and a review of thinning techniques

72%
Saeed K., Tabędzki M., Rybnik M., Adamski M.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 2
317-335
EN
This paper aims at three aspects closely related to each other: first, it presents the state of the art in the area of thinning methodologies, by giving descriptions of general ideas of the most significant algorithms with a comparison between them. Secondly, it proposes a new thinning algorithm that presents interesting properties in terms of processing quality and algorithm clarity, enriched with examples. Thirdly, the work considers parallelization issues for intrinsically sequential algorithms of thinning. The main advantage of the suggested algorithm is its universality, which makes it useful and versatile for a variety of applications.
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