An iterative method for split inclusion problems without prior knowledge of operator norms

In this paper, we study the approximation of solution (assuming existence) for the split inclusion problem in uniformly convex Banach spaces which are also uniformly smooth. We introduce an iterative algorithm in which the stepsizes are selected without the need for any prior information about the bounded linear operator norm and strong convergence obtained. The novelty of our algorithm is that the bounded linear operator norm is not given a priori and stepsizes are constructed step by step in a natural way. Our results extend and improve many recent and important results obtained in the literature on the split inclusion problem and its variations.