International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1982 / Article

Open Access

Volume 5 |Article ID 632643 | https://doi.org/10.1155/S0161171282000271

V. M. Sehgal, "A fixed point theorem for contraction mappings", International Journal of Mathematics and Mathematical Sciences, vol. 5, Article ID 632643, 4 pages, 1982. https://doi.org/10.1155/S0161171282000271

A fixed point theorem for contraction mappings

Received10 Nov 1980
Revised16 Feb 1981

Abstract

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.

Copyright © 1982 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.


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