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

Babu, G. V. R.; Prasad, K. N. V. V. Vara

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.

Reviewer: Vasile Berinde (Baia Mare)

MSC:

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

Keywords:

Banach space; Zamfirescu operator; fixed point; Mann iteration; Ishikawa iteration; rate of convergence

Citations:

Zbl 1036.47037

References:

[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