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A Note on Locally Expansive and Locally Accretive Operators

Published online by Cambridge University Press:  20 November 2018

Ricardo Torrejon
Ricardo Torrejon*
Affiliation:
Department of Mathematics and Computer Science, Southwest Texas State UniversitySan Marcos, Texas 78666
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Abstract

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Let X be a Banach space, D an open subset of X and Y a complete metric space. Assume that Y is metrically convex. For closed, locally m-expansive and mapping open subsets of D onto open subsets of Y, is is shown that y ∊ T(D) if and only if there exists x0 ∊ D such that d(Tx0, y) ≤ d(Tx, y) for all x ≤ ∂D.

Keywords

Primary 47H0647H15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 228 - 232
Copyright
Copyright © Canadian Mathematical Society 1983

References

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2. Kirk, W. A., and Schöneberg, R., Mappings Theorems for Local Expansions in Metric and Banach Spaces, J. Math. Anal. Appl. 72 (1979), 114–121.Google Scholar
3. Menger, K., Untersuchungen uber allgemeine Metrik, Math. Ann. 100 (1928), 75–163.Google Scholar
4. Schöneberg, R., On the Domain Invariance Theorem for Accretive Mappings, J. London Math. Soc. 24 (1981), 548–554.Google Scholar