Inexact generalized proximal point algorithm with alternating inertial steps for monotone inclusion problem

Abstract

In this paper, we propose and study an inexact generalized proximal point algorithm with alternated inertial steps for solving monotone inclusion problem and obtain weak convergence results under some mild conditions. In the case when the operator T is such that T-1 is Lipschitz continuous at 0, we prove that the sequence of the iterates is linearly convergent. Fejer monotonicity of even subsequences of the iterates is also obtained. Finally, we give some priori and posteriori error estimates of our generated sequences.