Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators. (English) Zbl 1090.47053

Berinde, Vasile

Fixed Point Theory Appl. 2004, No. 2, 97-105 (2004).

Author’s abstract: In the class of quasi-contractive operator satisfying Zamfirescu’s conditions, the most used fixed point iterative methods, that is the Picard, Mann and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the first two methods with respect to their convergence rate is obtained.

Reviewer: Poom Kumam (Bangkok)

MSC:

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

Keywords:

Picard iteration; Mann iteration; Zamfirescu’s conditions; quasi-contractive mappings