Newton-Kantorovich Convergence Theorem of a Modified Newton's Method Under the Gamma-Condition in a Banach Space

WOS: 000318283900004A Newton-Kantorovich convergence theorem of a modified Newton's method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fr,chet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton-Kantorovich convergence theorems shows high accuracy of our results