On the equivalence of Mann and Ishikawa iteration methods
نویسندگان
چکیده
منابع مشابه
On the Equivalence of Mann and Ishikawa Iteration Methods
The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...
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We show that for several classes of mappings Mann and Ishikawa iteration procedures with errors in the sense of Xu [14] are equivalent. It is worth to mention here that, our results are the extensions or generalizations of some known recent results about equivalences.
متن کاملThe Equivalence of Mann Iteration and Ishikawa Iteration for Non-lipschitzian Operators
We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.
متن کاملOn Equivalence between Convergence of Ishikawa––mann and Noor Iterations
In this paper, we prove the equivalence of convergence between the Mann–Ishikawa– Noor and multistep iterations for Φ− strongly pseudocontractive and Φ− strongly accretive type operators in an arbitrary Banach spaces. Results proved in this paper represent an extension and refinement of the previously known results in this area. Mathematics subject classification (2010): 47H09, 47H10, 47H15.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203110198