A remark on directional contractions

Authors:
W. A. Kirk and William O. Ray

Journal:
Proc. Amer. Math. Soc. **66** (1977), 279-283

MSC:
Primary 47H10

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454755-8

MathSciNet review:
0454755

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *X* be a Banach space and *D* a convex subset of *X*. A mapping is called a directional contraction if there exists a constant such that corresponding to each there exists for which . Tests for lipschitzianness are obtained which yield the fact that if a closed mapping is a directional contraction, then it must be a global contraction, and sufficient conditions are given under which a nonclosed directional contraction always has a fixed point.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454755-8

Keywords:
Contraction mapping,
directional contraction,
fixed point theorem

Article copyright:
© Copyright 1977
American Mathematical Society