AN ITERATIVE METHOD FOR SOLVING SPLIT GENERALIZED MIXED EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES

Our aim in this paper is to study split generalised mixed equilibrium and fixed point problems in a real Banach space with a view to analyze an iterative method for obtaining a solution of the split generalised mixed equilibrium problem and fixed point problem in a real Banach space using the Bregman distance approach. Furthermore, we introduce an iterative algorithm for approximating a common solution of split generalised mixed equilibrium problem and a fixed point problem for left Bregman strongly nonexpansive mapping and with our algorithm, we state and prove a strong convergence theorem for the approximation of a common element of the set of solutions of a split generalised mixed equilibrium problem and the set of solutions of a fixed point problem in the framework of a p-uniformly convex Banach space which is also uniformly smooth. Our result extends existing results on split equilibrium problems in the literature from the framework of real Hilbert spaces to p-uniformly convex Banach spaces which are also uniformly smooth.