Semilocal convergence of Modified Chebyshev-Halley method for nonlinear operators in case of unbounded third derivative

In the present discussion, we analyze the semilocal convergence of a class of modified Chebyshev-Halley methods under two different sets of assumptions. In the first set, we just assumed the bound of the second order Fréchet derivative in lieu of the third order. In the second set of hypotheses, the bound of the norm of the third order Fréchet derivative is assumed at initial iterate preferably supposed it earlier on the domain of the given operator along with fulfillment of the local $\omega$-continuity in order to prove the convergence, existence and uniqueness followed by a priori error bound. Two numerical experiments strongly support the theory included in this paper.