Expanding the applicability of Inexact Newton Methods under Smale’s (α, γ)-theory

We present a new semilocal convergence analysis for an Inexact Newton Method (INM) using Smale’s (α,γα,γ)-theory. Our approach is based on the concept of center-γ0γ0-condition. Developed sufficient convergence conditions are weaker and the error estimates are tighter than those proposed in earlier studies such as Shen and Li [30] and [31], Guo [22], Smale [33], [34] and [35], Morini [26], Argyros [2], [8] and [9] and Argyros and Hilout [12]. Numerical examples illustrating the theoretical results are also provided in this study.