Equations with smooth operators

M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii and V. Ya. Stetsenko

Chapter 3 in Approximate Solution of Operator Equations, 1972, pp 138-198 from Springer

Abstract: Abstract Consider the equation 11.1 $$Fx = 0,$$ 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.

Date: 1972
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DOI: 10.1007/978-94-010-2715-1_3

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