Journal of the
Korean Mathematical Society JKMS

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as \cite{1,2,3,4,5,6,7,8,9,10,11,12,13}, \cite{21,22}. Numerical examples are provided to illustrate the theoretical results.

Keywords: Steffensen's method, Banach space, fixed point, local-semilocal convergence, divided difference

MSC numbers: 47H10, 47J25, 47J05, 49M15, 65G99