EXTENDED FOUR PARAMETER CHEBYSHEV-HALLEY-TYPE METHODS OF ORDER SIX

A study of the local and the semilocal convergence is carried out for the Chebyshev-Halley-type iterative methods under ω-type condi tions. The conditions are imposed only on the first-order derivatives. In both cases, the convergence region and the region of uniqueness of the solution is established. The new technique is a usefull alternative to expensive Taylor series used to study the convergence of iterative methods requiring high order derivatives not on the methods. The re sults of a numerical experiment are presented to check the convergence conditions.