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.