The Ball-Picard Method A new algorithm for fixed-point problems

Nonexpansive mappings and iterative methods for finding their fixed points are an ongoing topic that receives a lot of attention from various areas such that optimization, signal processing and machine learning. Based on a very recent work by Kaja Gruntkowska et al., we propose a fixed-point approach of their idea which amounts to introduce a new method for solving fixed points of nonexpansive mappings. Then, we translate the developed analysis in optimization and monotone inclusion settings. Next, we suggest some further developments. This is a first draft of an idea to be shared, before most likely, a complete verification and possible complements.