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 (@a,@c)-theory. Our approach is based on the concept of center-@c"0-condition. Developed sufficient convergence conditions are weaker and the error estimates are tighter than those proposed in earlier studies such as Shen and Li [30,31], Guo [22], Smale [33-35], Morini [26], Argyros [2,8,9] and Argyros and Hilout [12]. Numerical examples illustrating the theoretical results are also provided in this study.

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