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An Inequality Implicit Function Theorem

Part of: Topological linear spaces and related structures Functions of several variables

Published online by Cambridge University Press:  09 April 2009

Kung-Fu Ng
Kung-Fu Ng
Affiliation:
Department of MathematicsThe Chinese University of Hong Kong, Hong Kong
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Abstract

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Let f be a continuous function, and u a continuous linear function, from a Banach space into an ordered Banach space, such that f − u satisfies a Lipschitz condition and u satisfies an inequality implicit-function condition. Then f also satisfles an inequality implicit-function condition. This extends some results of Flett, Craven and S. M. Robinson.

MSC classification

Secondary: 46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 26B10: Implicit function theorems, Jacobians, transformations with several variables 46A40: Ordered topological linear spaces, vector lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 146 - 150
Copyright
Copyright © Australian Mathematical Society 1988

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