International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 301-304

A fixed point theorem for contraction mappings

V. M. Sehgal

Department of Mathematics, University of Wyoming, Laramie 82071, Wyoming, USA

Received 10 November 1980; Revised 16 February 1981

Copyright © 1982 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 S be a closed subset of a Banach space E and f:SE be a strict contraction mapping. Suppose there exists a mapping h:S(0,1] such that (1h(x))x+h(x)f(x)S for each xS. Then for any x0S, the sequence {xn} in S defined by xn+1=(1h(xn))xn+h(xn)f(xn), n0, converges to a uS. Further, if h(xn)=, then f(u)=u.