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Inexact Newton’s method for generalized operator equations in Banach spaces

Singh V. K.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 4

85--97

In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton’s method as well as the inexact Newton method.