Éditeur(s) : HAL CCSD Résumé : International audience This paper deals with variational inclusions of the form 0 2 f(x) + g(x) K where f is smooth function from a re exive Banach space X into a Banach space Y , g is a Lipschitz function from X into Y and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by an extension of the Zincenko's method which can be seen as a perturbed Newton's method. Numerical results are given at the end of the paper. Revista Investigacion Operacional
Éditeur(s) : HAL CCSD Résumé : International audience This paper deals with variational inclusions of the form 0 ∈ K − f(x) − g(x) where f is a smooth function from a reflexive Banach space X into a Banach space Y , g is a function from X into Y admitting divided differences and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by a combination of two methods: the Newton and the Secant methods. We show that the order of the semilocal method obtained is equal to (1 + √5)/2. Numerical results are also given to illustrate the convergence at the end of the paper. Serdica Math. J.
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