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Relaxing convergence conditions for Stirling's method
Author(s) -
Parhi S. K.,
Gupta D. K.
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1164
Subject(s) - mathematics , lipschitz continuity , uniqueness , convergence (economics) , operator (biology) , fréchet derivative , nonlinear system , mathematical analysis , fixed point , hölder condition , type (biology) , banach space , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , economics , gene , economic growth , ecology , biology
The aim of this paper is to study the convergence of Stirling's method used for finding fixed points of nonlinear operator equations assuming that the first Fréchet derivative of the nonlinear operator be ω‐conditioned. The ω‐condition relaxes the Lipschitz/Hölder condition on the first Fréchet derivative used earlier for the convergence. The existence and uniqueness regions are derived for the fixed points. Finally, the efficacy of our convergence analysis is shown by working out an integral equation of Hammerstein type of second kind. The results obtained show that our approach finds better results when compared with the results obtained by Newton's method. Copyright © 2009 John Wiley & Sons, Ltd.