Semilocal convergence theorem by using majorizing functions for Harmonic mean Newton's method in Banach spaces

摘要

In this paper, we study the semilocal convergence of the Harmonic mean Newton's method for solving nonlinear equations in Banach spaces. We establish the Newton-Kantorovich-type convergence theorem for the method by using majorizing functions. We obtain an existence-uniqueness theorem and an error estimate. In comparison with the results obtained in Chen et al.,we can provide a larger convergence radius. Finally, some numerical applications is presented to demonstrate our approach.