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    Newton’s method for generalized equations using restricted domains

    Autor: 
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto
    Fecha: 
    2017
    Palabra clave: 
    computer science; mathematics & statistics; Scopus(2); WOS(2)
    Revista / editorial: 
    Iterative Methods and Their Dynamics with Applications: A Contemporary Study
    Tipo de Ítem: 
    bookPart
    URI: 
    https://reunir.unir.net/handle/123456789/10516
    DOI: 
    https://doi.org/10.1201/9781315153469
    Dirección web: 
    https://www.taylorfrancis.com/books/e/9781315153469
    Resumen:
    In this chapter we are concerned with the study of the generalized equation F(x)+Q(x) ϶ 0, where F : D → H is a nonlinear Fréchet differentiable defined on the open subset D of the Hilbert space H, and Q : H ⇉ H is set-valued and maximal monotone. Many problems from Applied Sciences can be solved finding the solutions of equations in a form like (12.1) [17-22,27,28,30,39]. If ψ : H → (−∞,+∞] is a strict lower semicontinuous convex function and Q(x) = ∂ψ(x) = {u ∈ H : ψ(y) ≥ ψ(x)+⟨u, y−x⟩}, for all y ∈ H, then (12.1) becomes the variational inequality problem F(x)+∂ψ(x) ϶ 0, including linear and nonlinear complementary problems, additional comments about such problems can be found in [1-32, 36-40].
    Descripción: 
    Capítulo del libro "Iterative Methods and Their Dynamics with Applications: A Contemporary Study"
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