WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 16, 2017
Convergence Analysis of an Extended Newton-type Method for Implicit Functions and Their Solution Mappings
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Abstract: Let P, X and Y be Banach spaces. Suppose that f : P × X → Y is continuously Frechet differentiable function depend on the point (p, x) and F : X ⇒ 2^Y 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 Frechet 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 (p, x).
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Keywords: Set-valued maps, Parametric generalized equations, Semilocal convergence, Lipschitz-like mappings, Solution mapping, Extended Newton-type method
Pages: 133-142
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #16