International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 553-563

Semilocal analysis of equations with smooth operators

George J. Miel

Department of Mathematical Sciences, University of Nevada, Las Vegas 89154, Nevada, USA

Received 2 September 1980

Copyright © 1981 George J. Miel. 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.


Recent work on semilocal analysis of nonlinear operator equations is informally reviewed. A refined version of the Kantorovich theorem for Newton's method, with new error bounds, is presented. Related topics are briefly surveyed.