Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula
نویسندگان
چکیده
This paper deals with variational inclusions of the form: 0 ∈ f(x)+F (x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ∈ f(xk)+ ∑M i=1 ai∇f ( xk+βi(xk+1−xk) ) (xk+1−xk)+F (xk+1) where the single-valued function involved in this relation is an approximation of the function f based on a multipoint iteration formula and we show that this method is locally cubically convergent.
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