Convergence Analysis of an Extended Newton-type Method for Implicit Functions and Their Solution Mappings
نویسنده
چکیده
Let P ,X and Y be Banach spaces. Suppose that f : P ×X → Y is continuously Fréchet differentiable function depend on the point (p, x) and F : X ⇒ 2 is a set-valued mapping with closed graph. Consider the following parametric generalized equation of the form: 0 ∈ f(p, x) + F (x). (1) In the present paper, we study an extended Newton-type method for solving parametric generalized equation (1). Indeed, we will analyze semi-local and local convergence of the sequence generated by extended Newton-type method under the assumptions that f(p, x), the Fréchet derivative Dxf(p, x) in x of f(p, x) are continuously depend on (p, x) and (f(p, ·) + F )−1 is Lipschitz-like at (p̄, x̄). Key–Words: Set-valued maps, Parametric generalized equations, Semilocal convergence, Lipschitz-like mappings, Solution mapping, Extended Newton-type method. AMS(MOS) Subject Classifications: 49J53, 47H04, 65K10.
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