On the stability of some fixed point procedures. (English) Zbl 1031.47030

Berinde, Vasile

Bul. Ştiinţ. Univ. Baia Mare, Ser. B, Fasc. Mat.-Inform. 18, No. 1, 7-14 (2002).

Summary: Following the concept of \(T\)-stability defined by us [“Generalized contractions and applications” (Romanian) (Colectia Universitaria, Editura Cub Press 22, Baia Mare) (1997; Zbl 0885.47022)] for a fixed point iteration procedure, we establish in a simpler manner the same stability results for the Picard iteration and Mann iteration considered in metric spaces and normed linear spaces, respectively.

MSC:

47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)
47J25	Iterative procedures involving nonlinear operators
65D15	Algorithms for approximation of functions

Keywords:

fixed point iteration; \(T\)-stability

Citations:

Zbl 0885.47022