Open AccessON AN APPLICATION OF A VARIANT OF THE CLOSED GRAPH THEOREM AND THE SECANT METHOD
Author(s) -
Ioannis K. Argyros
Publication year - 1993
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.24.1993.4496
Subject(s) - mathematics , lipschitz continuity , operator (biology) , secant method , graph , derivative (finance) , fréchet derivative , discrete mathematics , pure mathematics , newton's method , nonlinear system , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , financial economics , banach space , economics , gene
The method of nondiscrete mathematical induction is used to find error bounds for the Secant method. We assume only that the operator has Holder continuous derivatives. In the case the Frechet derivative of the operator satisfies a Lipschitz condition our results reduce to the ones obtained by F. Potra (Num. Math. 1982).