On split equality variation inclusion problems in Banach spaces without operator norms

Document Type : Research Paper

Authors

1 University of KwaZulu-Natal

2 University of KwaZulu-Natal University Road Westville Durban South Africa

Abstract

The purpose of this paper is to study the approximation of solutions of split equality variational inclusion problem in uniformly convex Banach spaces which are also uniformly smooth. We introduce an iterative algorithm in which the stepsize does not require prior knowledge of operator norms. This is very important in practice because norm of operators that are often involved in applications are rarely known explicitly. We prove a strong convergence theorem for the approximation of solutions of split equality variational inclusion problem in $p$-uniformly convex Banach spaces which are also uniformly smooth. Further, we give some applications and a numerical example of our main theorem to show how the sequence values affect the number of iterations. Our results improve, complement and extend many recent results in literature.

Keywords