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

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

Zbl 0885.47022