6 papers
Rates of metastability for iterations on the unit interval
Andrei Sipos
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, firstl…
The finitary content of sunny nonexpansive retractions
Ulrich Kohlenbach, Andrei Sipos
We use techniques of proof mining to extract a uniform rate of metastability (in the sense of Tao) for the strong convergence of approximants to fixed points of uniformly continuou…
Effective strong convergence of the proximal point algorithm in CAT(0) spaces
Laurentiu Leustean, Andrei Sipos
We apply methods of proof mining to obtain uniform quantitative bounds on the strong convergence of the proximal point algorithm for finding minimizers of convex, lower semicontinu…
The asymptotic behaviour of convex combinations of firmly nonexpansive mappings
Andrei Sipos
We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive -- or which satisfy the more general property -- is asy…
An application of proof mining to the proximal point algorithm in CAT(0) spaces
Laurentiu Leustean, Andrei Sipos
We compute, using techniques originally introduced by Kohlenbach, the first author and Nicolae, uniform rates of metastability for the proximal point algorithm in the context of CA…
Effective results on a fixed point algorithm for families of nonlinear mappings
Andrei Sipos
We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by López-Acedo and Xu to find common fixed points o…