International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 241-246
doi:10.1155/S0161171285000266

Perturbations of normally solvable nonlinear operators. I

Abstract

Let X and Y be Banach spaces and let ℱ and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.