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Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces. (English) Zbl 1364.47026
Summary: We introduce a new three-step iteration scheme and prove that this new iteration scheme is convergent to fixed points of contractive-like operators. Also, by providing an example, we show that our new iteration method is faster than another iteration method due to S. Suantai [J. Math. Anal. Appl. 311, No. 2, 506–517 (2005; Zbl 1086.47057)]. Furthermore, it is shown that this new iteration method is equivalent to some other iteration methods in the sense of convergence. Finally, it is proved that this new iteration method is $$T$$-stable.

##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 65J15 Numerical solutions to equations with nonlinear operators
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