Abstract:
In this paper, we investigate a shrinking algorithm for finding a solution of split monotone variational
inclusion problem which is also a common fixed point problem of relatively nonexpansive mapping
in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm
employed in this paper is design in such a way that it does not require prior knowledge of operator
norm. We prove a strong convergence result for approximating the solutions of the aforementioned
problems and give applications of our main result to split convex minimization problem. The result
present in this paper extends and complements many related results in literature.
