OPERATOR NORM INDEPENDENT SOLUTION OF SPLIT EQUALITY EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR CERTAIN MULTIVALUED MAPS

In this paper, we introduce a new multivalued k-strictly pseudononpsreading mapping T with type-one condition and prove that the set of fixed points of T is closed and convex. We also proved that I − T is demiclosed at zero without the condition that the set of fixed point of T is strict. Using this new mapping, we study the strong convergence of a new iterative algorithm for approximating a common element of the set of solutions of a system of split equality generalized mixed equilibrium problems and fixed point problem of k-strictly pseudononspreading multivalued type-one mappings without a prior knowledge of the operator norm in real Hilbert space. Furthermore, we give a numerical example of our main theorem in real Hilbert spaces. Our result improves and complements some recent corresponding results in the literature.