Strong Convergence Theorems for Resolvents of Accretive Operators with Possible Unbounded Errors

In this paper, we study the convergence analysis of the sequence generated by an inexact proximal point method with unbounded errors to find zeros of m-accretive operators in Banach spaces. We prove the zero set of the operator is nonempty if and only if the generated sequence is bounded. In this case, we show that the generated sequence converges strongly to a zero of the operator. This process defines a sunny nonexpansive retraction from the Banach space onto the zero set of the operator. We present also some applications and numerical experiments for our results.