Hybrid inertial viscosity-type forward-backward splitting algorithms for variational inclusion problems

Herein, we aimed to develop two hybrid inertial viscosity-type forward-backward splitting algorithms for estimating the common solution of the variational inclusion problem and fixed point problem in Hilbert spaces. At the beginning of each iteration, the first algorithm estimated viscosity, fixed point, and inertial extrapolation. On the other hand, the second method estimated viscosity and inertial extrapolation alone. We demonstrated that the sequence induced by the proposed hybrid algorithms has strong convergence. We discussed a few special cases of the proposed algorithms and also presented theoretical applications of our findings. We furnished suitable numerical examples to validate the effectiveness of the recommended approaches.