An iterative method for solving split minimization problem in Banach space with applications

The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in $p$-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.