Abstract
In this chapter we want to study the following topics.
For any continuous function f: ℝ → ℝ growing everywhere strictly faster than the function g(x) = x, the equation has a unique solution. This solution can be obtained by the iteration method , where t is a sufficiently small positive number.
The purpose of this note is to show that the above theorem, and its corresponding local form, remain valid in Hilbert spaces, provided the notion of a function growing faster than another is adequately extended.
A fundamental tool in our argument is the Banach fixed-point theorem.
Eduardo Zarantonello (1960)
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Zeidler, E. (1990). Lipschitz Continuous, Strongly Monotone Operators, the Projection-Iteration Method, and Monotone Potential Operators. In: Nonlinear Functional Analysis and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0981-2_1
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