Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators
نویسندگان
چکیده
منابع مشابه
Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are convergent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained.
متن کاملPicard Iteration Converges Faster than Mann Iteration for a Class of Quasi-contractive Operators
In the last three decades many papers have been published on the iterative approximation of fixed points for certain classes of operators, using the Mann and Ishikawa iteration methods, see [4], for a recent survey. These papers were motivated by the fact that, under weaker contractive type conditions, the Picard iteration (or the method of successive approximations), need not converge to the f...
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We establish a general theorem to approximate fixed points of quasi-contractive operators on a normed space through the three-step iteration process. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].
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A convergence theorem of Rhoades [18] regarding the approximation of fixed points of some quasi contractive operators in uniformly convex Banach spaces using the Ishikawa iterative procedure, is extended to arbitrary Banach spaces. The conditions on the parameters {αn} that define the Ishikawa iteration are also weakened.
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ژورنال
عنوان ژورنال: International Journal of Computer Applications
سال: 2013
ISSN: 0975-8887
DOI: 10.5120/11473-7082