A semilocal convergence analysis of an inexact Newton method using recurrent relations

We extend the applicability of an inexact Newton method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The recurrent relations method is used to prove the existence-convergence theorem. Our error bounds are tighter and the information on the location of the solution at least as precise under the same information as before. Our results compare favorably with earlier studies in [1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20]. A numerical example involving a nonlinear integral equation of a Chandrasekhar type is also presented in this stud