Tikhonov-regularized extrapolated viscosity method: applications to economic equilibrium and signal recovery

The purpose of this paper is to design a novel iterative algorithm to solve a generalized split feasibility and fixed point problem with multiple output sets (GSFFPPM) in the framework of Hilbert spaces. The proposed algorithm combines inertial extrapolation and the S-iterative methodology to accelerate convergence, Tikhonov regularization to ensure stability, and viscosity approximation to guarantee strong convergence to a solution of the GSFFPPM. Due to the generality of our model, we demonstrate the applicability of our iterative method to important classes of problems, including split variational inclusions and split equilibrium problems. To illustrate the practical relevance and computational efficiency of the proposed method, we present numerical experiments on real-world models such as Nash–Cournot semi-oligopolistic market equilibria and signal recovery tasks. These numerical experiments demonstrate the robustness and effectiveness of the proposed method.