  A new one-parameter family of iterative method for solving nonlinear
equations is constructed and studied. Two variants, both with cubic
convergence, are developed, one for finding simple zeros and other for multiple
zeros of known multiplicities. This family generates a variety of different
third order methods, including Halley-like method as a special case. Four
numerical examples are given to demonstrate convergence properties of the
proposed methods for multiple zeros and various values of the parameter.
