Solving a General Split Equality Problem Without Prior Knowledge of Operator Norms in Banach Spaces

Abstract

In this paper, using Bregman distance, we introduce an iterative algorithm for approximating a common solution of Split Equality Fixed Point Problem and Split Equality Equilibrium Problem in p-uniformly convex and uniformly smooth Banach spaces that are more general than Hilbert spaces. The advantage of the algorithm is that it is done without the prior knowledge of Bregman Lipschitz coefficients and operator norms. The strong convergence of the algorithm is established under mild assumptions. As special cases, we shall utilize our results to study the Split Equality Null point Problems and Split Equality Variational Inequality Problems. A numerical example is given to demonstrate the convergence of the algorithm. Our results complement and extend some related results in the literature.