On the convergence of efficient King-Werner-type methods of order 1+2

We present a local as well as a semilocal convergence analysis of some efficient King-Werner-type methods of order 1+2 in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our results compare favorably to earlier results using the same or stronger hypotheses (McDougall and Wotherspoon, 2014; Werner, 1979, 1982). Numerical examples are also presented to illustrate the theoretical results.