An extension of A. Ostrowski’s theorem on the round-off stability of iterations. (English) Zbl 0885.47023

Jachymski, Jacek R.

Aequationes Math. 53, No. 3, 242-253 (1997).

Summary: A. M. Ostrowski established the stability of the procedure of successive approximations for Banach contractive maps. In this paper, we generalize the above result by using a more general contractive definition introduced by F. Browder. Further, we study the case of maps on metrically convex metric spaces and compact metric spaces, obtaining results relative to fixed point theorems of D. W. Boyd and J. S. W. Wong, and M. Edelstein. Finally, as a by-product of our basic lemma, we extend a recent result of T. Vidalis concerning the convergence of an iteration procedure involving an infinite sequence of maps.

MSC:

47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)
65D15	Algorithms for approximation of functions

Keywords:

stability of the procedure of successive approximations; Banach contractive maps; metrically convex metric spaces; compact metric spaces; fixed point theorems; convergence of an iteration procedure

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