A differentiable characterization of local contractions on Banach spaces

Hefti, Andreas

doi:10.21256/zhaw-3994

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-3994

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	A differentiable characterization of local contractions on Banach spaces
Authors:	Hefti, Andreas
DOI:	10.21256/zhaw-3994 10.1186/s13663-015-0349-7
Published in:	Fixed Point Theory and Applications
Volume(Issue):	2015
Issue:	106
Page(s):	1
Pages to:	5
Issue Date:	2015
Publisher / Ed. Institution:	Springer
ISSN:	1687-1812
Language:	English
Subjects:	Contraction mapping; Spectral radius; Attractive fixed point; Local stability; Difference equation
Abstract:	This note provides a differentiable characterization of local contractions on an arbitrary Banach space. As a corollary, a refinement to Ostrowski’s sufficient condition for local convergence in finite spaces is obtained, which applies to many models, e.g. in economics, ecology or game theory, where one has an interest in fixed point iterations and local stability of discrete dynamic processes. We show that for the local contraction property to hold, continuity of the derivative at the fixed point is indispensable.
URI:	https://digitalcollection.zhaw.ch/handle/11475/11176
Fulltext version:	Published version
License (according to publishing contract):	CC BY 4.0: Attribution 4.0 International
Departement:	School of Management and Law
Organisational Unit:	Center for Energy and Environment (CEE)
Appears in collections:	Publikationen School of Management and Law

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Hefti, A. (2015). A differentiable characterization of local contractions on Banach spaces. Fixed Point Theory and Applications, 2015(106), 1–5. https://doi.org/10.21256/zhaw-3994

Hefti, A. (2015) ‘A differentiable characterization of local contractions on Banach spaces’, Fixed Point Theory and Applications, 2015(106), pp. 1–5. Available at: https://doi.org/10.21256/zhaw-3994.

A. Hefti, “A differentiable characterization of local contractions on Banach spaces,” Fixed Point Theory and Applications, vol. 2015, no. 106, pp. 1–5, 2015, doi: 10.21256/zhaw-3994.

HEFTI, Andreas, 2015. A differentiable characterization of local contractions on Banach spaces. Fixed Point Theory and Applications. 2015. Bd. 2015, Nr. 106, S. 1–5. DOI 10.21256/zhaw-3994

Hefti, Andreas. 2015. “A Differentiable Characterization of Local Contractions on Banach Spaces.” Fixed Point Theory and Applications 2015 (106): 1–5. https://doi.org/10.21256/zhaw-3994.

Hefti, Andreas. “A Differentiable Characterization of Local Contractions on Banach Spaces.” Fixed Point Theory and Applications, vol. 2015, no. 106, 2015, pp. 1–5, https://doi.org/10.21256/zhaw-3994.