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History of the Banach Fixed Point Theorem

Fimmtudaginn, 14. september 2023 - 16:30
Askja, stofa 132

Małgorzata Terepeta, prófessor við Tækniháskólann í Łódź heldur fyrirlestur fyrir Íslenska stærðfræðafélagið. Kaffi og spjall hefst kl. 16:30 og fyrirlesturinn sjálfur hefst kl. 17.

Ágrip: On June 24, 1920 Stefan Banach presented his doctoral dissertation titled operacjach na zbiorach abstrak-cyjnych i ich zastosowaniach do równań całkowych(On operations on abstract sets and their applications tointegral equations) to the Philosophy Faculty of Jan Kazimierz University in Lvov. He passed his PhD exami-nations in mathematics, physics and philosophy, and in January 1921 he received his PhD degree. A year later,he published the results of his doctorate in Fundamenta Mathematicae. Among them there was the theoremknown today as the Banach Fixed Point Theorem or the Banach Contraction Principle. It is one of the mostfamous theorems in mathematics, one of many under the name of Banach. It concerns certain mappings (calledcontractions) of a complete metric space into itself and it gives the conditions sufficient for the existence anduniqueness of a fixed point of such mapping. In 2022 we had a centenary of publishing this theorem and we in thetalk there will be presented its most important modifications and generalizations, several contractive conditions,the converse theorems and some applications.