Enclosing roots of polynomial equations and their applications to iterative processes.
Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
2000 Mathematics Subject Classification: 47H04, 65K10. In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.
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