Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators. (English) Zbl 1106.47053

Fixed Point Theory Appl. 2006, Article 49615, 6 p. (2006); erratum ibid. 2007, Article ID 97986, 2 p. (2007).
The concept of rate of convergence for fixed point iteration procedures, introduced and studied by the reviewer [cf.V. Berinde, “Iterative approximation of fixed points” (Efemeride, Baia Mare) (2002; Zbl 1036.47037)] is used to compare the speed of convergence of two of the most studied fixed point iterations, i.e., the Mann and Ishikawa iterations, in the class of Zamfirescu operators.


47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)


Zbl 1036.47037
Full Text: DOI EuDML


[1] Berinde V: Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare; 2002:xii+283. · Zbl 1036.47037
[2] Berinde V: On the convergence of the Ishikawa iteration in the class of quasi contractive operators.Acta Mathematica Universitatis Comenianae. New Series 2004,73(1):119-126. · Zbl 1100.47054
[3] Berinde, V., Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, 97-105 (2004) · Zbl 1090.47053
[4] Berinde V: On the convergence of Mann iteration for a class of quasicontractive operators. in preparation, 2004
[5] Zamfirescu T: Fix point theorems in metric spaces.Archiv der Mathematik 1992, 23: 292-298. · Zbl 0239.54030
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