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On new three-step iterative scheme for approximating the fixed points of non-expansive mappings. (English) Zbl 1382.47013
Summary: In the present paper, we introduce a new three-step fixed point iterative scheme for approximating the fixed points of non-expansive mappings. Here, we prove that the rate of convergence of our proposed iterative scheme is faster than that of Picard, Mann, Ishikawa, Agarwal et al., Abbas et al. and Thakur et al. iterative schemes. To support the analytic proof and the proper comparison of our proposed iterative scheme, we discuss a numerical example of D. Thakur et al. [J. Inequal. Appl. 2014, Paper No. 328, 15 p. (2014; Zbl 1353.47111)] in which we approximate the fixed point by using a Matlab program. Finally, we establish some convergence theorems for the non-expansive mappings by using our proposed iterative scheme.
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
Matlab
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