Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 34, No 2, (2008), 455p-466p
Abstract:
We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].