Multi-inertial parallel hybrid projection algorithm for generalized split null point problems

In this paper we suggest a theoretical framework to study the generalized split null point problem (GSNPP) via a multi-step inertial based parallel hybrid projection algorithm in Hilbert spaces. The architecture and the suitable set of control conditions ensure the strong convergence of the algorithm. The possible applications of the algorithm are illustrated via various theoretical and numerical results. The key advantages of the algorithm are highlighted in comparison to the classical and non-inertial algorithm as well as (one-step and two-step) inertial variants of the algorithm for the GSNPP.