Equations with smooth operators
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Consider the equation
where F is a Fréchet-differentiable nonlinear operator mapping a subset ℜ of a Banach space E1 into a Banach space E2. We shall find it convenient to assume that ℜ is a ball. The principal method for constructing successive approximations x n to a solution x* (if it exists) of equation (11.1) is based on successive linearization of the equation.
$$Fx = 0,$$
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