International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 241-246

Perturbations of normally solvable nonlinear operators, I

William O. Ray and Anita M. Walker

Department of Mathematics, The University of Oklahoma, Norman 73019, OK, USA

Received 16 January 1984

Copyright © 1985 William O. Ray and Anita M. Walker. 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 X and Y be Banach spaces and let and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator +𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator The methods extend previous results in the area of normal solvability for nonlinear operators.