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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 663-667
http://dx.doi.org/10.1155/S0161171285000722

On fixed points of set-valued directional contractions

Department of Mathematics, Seoul National University, Seoul 151, South Korea

Received 4 June 1984; Revised 25 April 1985

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using equivalent formulations of Ekeland's theorem, we improve fixed point theorems of Clarke, Sehgal, Sehgal-Smithson, and Kirk-Ray on directional contractions by giving geometric estimations of fixed points.