A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES

Abstract

In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformlyconvex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizesusually depend on the knowledge of the operator norm or Lipschitz constant, a nice featureof the proposed algorithm is the fact that it requires only a diminishing and non-summablestep-size to obtain strong convergence of the iterates to a solution of the problem. Finally,the proposed algorithm is implemented in the setting of a classical Banach space to supportthe theory established.