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Convergence of Stirling's method under weak differentiability condition
Author(s) -
Parhi S. K.,
Gupta D. K.
Publication year - 2010
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.1345
Subject(s) - mathematics , uniqueness , fixed point , banach space , fréchet derivative , convergence (economics) , operator (biology) , differentiable function , mathematical analysis , fixed point theorem , nonlinear system , economic growth , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , economics , gene
The aim of this paper is to establish the semilocal convergence analysis of Stirling's method used to find fixed points of nonlinear operator equations in Banach spaces. This is done by using recurrence relations under weak Hölder continuity condition on the first Fréchet derivative of the involved operator. The existence and uniqueness regions for a fixed point are obtained. The efficacy of our work is demonstrated by solving an integral equation of Hammerstein type and comparing the results obtained by Newton's method. It is found that our approach gives better existence and uniqueness regions for a fixed point. Copyright © 2010 John Wiley & Sons, Ltd.