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Convexity and almost convexity in groups

100%

Jarczyk W.

Banach Center Publications

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2013

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tom 99

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nr 1

55-76

EN

We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance the problem of the extendibility of a convex function from a subgroup to the whole group. What concerns almost convexity we present an abstract version of Kuczma's theorem. We sketch also some possible applications in improving regularity of solutions of a difference equation and in integer programming. The first appears, among others, in probability while determining weak generalized stable distributions, whereas the second is important in economics.

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On solutions of a certain functional-integral equation

44%

Jarczyk W.

Annales Polonici Mathematici

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1984

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tom 44

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nr 1

51-65

3

Generic properties of some iterative functional equations

44%

Jarczyk W.

Annales Polonici Mathematici

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1986-1987

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tom 47

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nr 3

361-369

4

On linear homogeneous functional equations in the indeterminate case

44%

Jarczyk W.

Fundamenta Mathematicae

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1984

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tom 120

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nr 2

99-104

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Banach Center Publications

1 Fundamenta Mathematicae

4 Jarczyk W.

1 2013

1 1987

2 1984

Convexity and almost convexity in groups

On solutions of a certain functional-integral equation

Generic properties of some iterative functional equations

On linear homogeneous functional equations in the indeterminate case