The purpose of this paper is to introduce a simultaneous iterative algorithm for solving split equality for systems of generalized mixed equilibrium problem and split equality fixed point problem in $p$-uniformly convex and uniformly smooth Banach spaces using the Bregmann distance technique. Furthermore, we state and prove a strong convergence theorem for the approximation of a solution of split equality for systems of generalized mixed equilibrium problem and split equality fixed point problem in the frame work of $p$-uniformly convex and uniformly smooth Banach spaces. Our result extends results on split equality generalized mixed equilibrium problems from Hilbert spaces to $p$-uniformly convex Banach spaces which are also uniformly smooth.