Rates of metastability for iterations on the unit interval

Abstract

We use techniques of proof mining to extract computable and uniform rates of metastability (in the sense of Tao) for iterations of continuous functions on the unit interval, firstly (following earlier work of Gaspar) out of convergence proofs due to Franks, Marzec, Rhoades and Hillam and then out of an argument due to Borwein and Borwein that pertains only to Lipschitz functions.