Abstract
This paper is devoted to Newton–Steffensen–type method for
approximating the unique solution of perturbed nonsmooth subanalytic
variational inclusion in finite–dimensional spaces. We use a combination of Newton’s method studied by Bolte et al. [14] for locally Lipschitz subanalytic function in order to solve nonlinear equations, with
Steffensen’s method [1, 2, 3, 9, 19]. Using the Lipschitz–like concept of
set–valued mappings, the subanalyticity hypothesis on the involved function and some condition on divided difference operator, the superlinear
convergence is established. We also present a finer convergence analysis
using some ideas introduced by us in [4, 7, 8] for nonlinear equations. Finally, we present some new regula–falsi–type method for set–valued map.
Ioannis K. Argyros, Sa¨ıd Hilout. (2013) Newton–Steffensen–Type Method for Perturbed Nonsmooth Subanalytic Variational Inequalities, Punjab University Journal of Mathematics, Volume 45, Issue 1.
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