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The paper is concerned with the convergence problem of Newton type methods for finding zeros of nonlinear operators in Banach spaces. Some families of nonlinear operators redefined by different Lipschitz conditions and an “universal constant” is introduced so that unified convergence determination of these methods is established for the defined families.
The theory of “point estimate” and the concept of “general convergence”, which were put forward by Smale in order to investigate the complexity of algorithms for solving equations, have been producing a deep impact on the research about the local behavior, the semi-local behavior and the global behavior of iteration methods. The criterion of point estimate introduced by him not only provides a tool...
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