Open AccessA sharpened form of the inverse function theorem
Author(s) -
Mark Elin,
David Shoikhet
Publication year - 2020
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2019.73.2.59-67
Subject(s) - inverse function , inverse , convexity , inverse function theorem , mathematics , function (biology) , range (aeronautics) , implicit function theorem , inverse demand function , inverse problem , mathematical analysis , pure mathematics , picard–lindelöf theorem , geometry , fixed point theorem , demand curve , engineering , evolutionary biology , financial economics , economics , biology , aerospace engineering , microeconomics
In this note we establish an advanced version of the inverse function theorem and study some local geometrical properties like starlikeness and hyperbolic convexity of the inverse function under natural restrictions on the numerical range of the underlying mapping.