Abstract
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 study
