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A class of majorant functions for contractors and equations

Published online by Cambridge University Press:  17 April 2009

Mieczyslaw Altman
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales and Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana, USA.
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Majorant functions for contractors can be defined in a natural war. Such a case is considered here in order to find iterative solutions of general equations in Banach spaces by means of contractors. A class of majorant functions is defined which contains in particular the linear majorant ones. Local and global existence and convergence theorems are proved.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Altman, M., “Inverse differentiability contractors and equations in Banach spaces”, Studia Math. 46 (1973), 115.Google Scholar
[2]Altman, Mieczyslaw, “Contractors with nonlinear majorant functions and equations in Banach spaces”, Bull. Un. Mat. Ital. (to appear).Google Scholar