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On the Secant method under generalized Lipschitz conditions for the divided difference operator
Author(s) -
Shakhno Stepan
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701142
Subject(s) - lipschitz continuity , mathematics , uniqueness , operator (biology) , mathematical analysis , integrable system , lipschitz domain , ball (mathematics) , banach space , pure mathematics , chemistry , biochemistry , repressor , transcription factor , gene
In this work we introduce for the first time the generalized Lipschitz conditions for the divided difference operator. A positive integrable function, partial case of which is usual Lipschitz constant, is suggested. Under the given conditions the convergence of the Secant method for solving the operator equations in Banach spaces is investigated, the uniqueness ball for the solution is obtained. As a partial case the known results for the Lipschitz constants are received. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)