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Semilocal convergence for the Super-Halley’s method
Numerical Analysis and Applications, 2014Summary: The semilocal convergence of the super-Halley's method for solving nonlinear equations in Banach spaces is established under the assumption that the second Fréchet derivative satisfies the \(\omega\)-continuity condition. This condition is milder than the well-known Lipschitz and Hölder continuity conditions. The importance of our work lies in
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A new semilocal convergence theorem of Müller’s method
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On the semilocal convergence of damped Newton’s method
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Semilocal Convergence Theorem for a Newton-like Method
East Asian Journal on Applied Mathematics, 2017AbstractThe semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-calledγ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate.
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