Results of Tadeusz Świątkowski on algebraic sums of sets and their applications in the theory of subadditive functions

• Autorzy: Matkowski J.
• Języki publikacji: EN

Abstrakty

EN

A refinement of Steinhaus' theorem on the algebraic sum of subsets of R due to Raikov (1939) was not known to the mathematical community and still is not popular. In 1994, Tadeusz Świątkowski, being not aware of the existence of Raikov's theorem, proved another result of this type. Unfortunately, a few days later he passed away. In this paper we present the theorems of Świątkowski and Raikov and we apply them in the theory of subadditive type inequalities. An improvement of a converse of Minkowski's inequality theorem is presented.

Słowa kluczowe

EN

algebraic sum of sets; density of set at a point; interior point; Steinhaus theorem; Raikov theorem; subadditive function

PL

algebraiczna suma zbiorów; gęstość zbioru w punkcie; punkt wewnętrzny; twierdzenie Steinhausa; twierdzenie Raikova; funkcja podaddytywna

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2012
• Tom: Vol. 18, nr 1
• Strony: 97--116
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Matkowski J.

• Institute of Mathematics, Informatics and Econometry, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland,

Bibliografia

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