An improved local convergence analysis for Newton-Steffensen-type method (Q2379888)

The authors consider a Newton-Steffensen type algorithm for approximating the locally solution \(x^*\) of nonsmooth inexact variational inclusions in Banach spaces \[ 0\in F(x) + H(x) + G(x), \] where \(F: D\rightarrow X\) is differentiable in a neighborhood of the solution \(x^*\), \(H: D\rightarrow X\) is Fréchet differentiable at \(x=x^*\), and \(G\) is set valued map. The authors prove that the Newton-Steffensen method is locally linearly convergent with less computational cost and using weaker conditions than in the work by \textit{S. Hilout} [J. Math. Anal. Appl. 339, No.~2, 753--761 (2008; Zbl 1136.65057)].