International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 287-292

Approximating common fixed points of families of quasi-nonexpansive mappings

M. K. Ghosh1 and Lokenath Debnath2

1Department of Mathematics, Narajole Raj College, Midnapur, W B., India
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA

Received 26 September 1993; Revised 10 October 1994

Copyright © 1995 M. K. Ghosh and Lokenath Debnath. 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.


This paper deals with a family of quasi-nonexpansive mappings in a uniformly convex Banach space, and the convergence of iterates generated by this family. A fixed point theorem for two quasi-nonexpansive mappings is then proved. This theorem is then extended for a finite family of quasinonexpansive mappings. It is shown that Ishikawa's [1] result follows as special cases of results proved in this paper.