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Open mappings and solvability of nonlinear equations in Banach space

Published online by Cambridge University Press:  14 November 2011

Stewart C. Welsh
Stewart C. Welsh
Affiliation:
Department of Mathematics, Southwest Texas State University, San Marcos, TX 78666, U.S.A.
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Extract

We give sufficient conditions under which a funclion f: X → Y is an open mapping, where X and y are Banach spaces. This function is not necessarily continuous, but is assumed to have closed graph. We prove our results without requiring that f be Gateaux differentiable; instead, f is assumed to possess a weak type of Gateaux inverse derivative.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 239 - 246
Copyright
Copyright © Royal Society of Edinburgh 1996

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