Proof mining in metric fixed point theory and ergodic theory

TL;DR

This survey explores recent applications of proof mining techniques to fixed point theory of nonexpansive mappings and the metastability of ergodic averages in uniformly convex Banach spaces, highlighting new insights and methods.

Contribution

It introduces novel proof mining applications to fixed point and ergodic theories, providing new bounds and metastability results in these areas.

Findings

Enhanced bounds for fixed point iterations

New metastability results for ergodic averages

Applications to uniformly convex Banach spaces

Abstract

In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach spaces.