Double inertial subgradient extragradient algorithm for solving equilibrium problems and common fixed point problems with application to image restoration

This paper presents a double inertial method for solving equilibrium problems and common fixed point problems in Hilbert spaces. On the basis of the subgradient extragradient method, we modify the self adaptive rule and use an additional parameter to select appropriate step size. Under reasonable assumptions, we establish both weak and linear convergence properties for the proposed algorithm. Finally, numerical experiments are conducted to validate the rationality and effectiveness of the proposed method over the existing ones in the literature.