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On Existence Theorems for Solutions of Non‐Linear Systems
Author(s) -
Mayer Jan
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310227
Subject(s) - mathematics , norm (philosophy) , comparison theorem , zero (linguistics) , pure mathematics , function (biology) , mathematical analysis , calculus (dental) , discrete mathematics , law , medicine , linguistics , philosophy , dentistry , evolutionary biology , political science , biology
An equivalent formulation of a recent result in [1] states that if the conditions of the Theorem of Newton‐Kantorovich are satisfied in a slightly modified (but equivalent) form in the maximum norm for a function g : G → ℝ n , G ⊆ ℝ n , guaranteeing the existence of a zero in D, then the conditions of Miranda's Theorem are automatically satisfied. We prove that this result holds for arbitrary norms if the conditions of the Theorem of Newton‐Kantorovich are suitable strengthened and Miranda's Theorem is suitably generalized.