Back Fixpunktsatz vom Banach BAR Teorema del punt fix de Banach Catalan Banachova věta o pevném bodě Czech Theorem pwynt sefydlog Banach Welsh Fixpunktsatz von Banach German Teorema del punto fijo de Banach Spanish نظریه نقطه ثابت باناخ Persian Banachin kiintopistelause Finnish משפט נקודת השבת של בנך HE Banach fixponttétele Hungarian
In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points. It can be understood as an abstract formulation of Picard's method of successive approximations.[1] The theorem is named after Stefan Banach (1892–1945) who first stated it in 1922.[2][3]
- ^ Kinderlehrer, David; Stampacchia, Guido (1980). "Variational Inequalities in RN". An Introduction to Variational Inequalities and Their Applications. New York: Academic Press. pp. 7–22. ISBN 0-12-407350-6.
- ^ Banach, Stefan (1922). "Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales" (PDF). Fundamenta Mathematicae. 3: 133–181. doi:10.4064/fm-3-1-133-181. Archived (PDF) from the original on 2011-06-07.
- ^ Ciesielski, Krzysztof (2007). "On Stefan Banach and some of his results" (PDF). Banach J. Math. Anal. 1 (1): 1–10. doi:10.15352/bjma/1240321550. Archived (PDF) from the original on 2009-05-30.