International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 473-480
A pointwise contraction criteria for the existence of fixed points
Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USA
Received 7 May 1979
Copyright © 1979 V. M. Sehgal. 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.
Let be a subset of a metric space and be a mapping. In this paper, we define the notion of lower directional increment of at in the direction of and give sufficient conditions for to have a fixed point when for each . The results herein generalize the recent theorems of Clarke (Caned. Math. Bull. Vol. 21(1), 1978, 7-11) and also improve considerably some earlier results.