A theorem on mean-value iterations
Authors: R. L. Franks and R. P. Marzec
Journal: Proc. Amer. Math. Soc. 30 (1971), 324-326
MSC: Primary 26.54; Secondary 65.00
MathSciNet review: 0280656
Abstract: In this paper we consider a function which continuously maps a closed interval of the real line into itself. It is shown that a particular mean-value iterative scheme always converges to a fixed point. The result is known for functions which have a unique fixed point. This condition is not required here.