SOLVING SPLIT EQUALITY EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES WITHOUT PRIOR KNOWLEDGE OF THE OPERATOR NORMS

The purpose of this paper is to study the approximation of solution of split equality generalized mixed equilibrium problem and fixed point problem for right Bregman strongly quasi-nonexpansive mappings in q-uniformly convex Banach spaces which are also uniformly smooth. We introduce a simultaneous algorithm and prove strong convergence without prior information of the operator norms involved. This is very important because norms of bounded linear operators are rarely know explicitly. We also give applications of our result to approximation of solution of split equality mixed convex differentiable minimization problem and split equality feasibility fixed point problem in Banach spaces. Our result in this paper improve and extend many results on split equality fixed point problem and common solution of split equality fixed point and equilibrium problems in literature.