New Iteration Algorithms for Solving Equilibrium Problems and Fixed Point Problems of Two Finite Families of Asymptotically Demicontractive Multivalued Mappings

ln this paper, we introduce a new class of mapping called asymptotically demicontractive multivalued mapping in the setting of a real Hilbert space. Furthermore, a new iteration scheme was constructed and it was proved that our algorithm converges strongly to the common element of solutions of an equilibrium prob-lem and the set of common fixed points of two finite families of type -one asymptotically demicontractive multivalued mappings without any sum conditions imposed on the finite family of the control se-quences. Also, we provided a numerical example to demonstrate the implementablity of our proposed iteration technique. Our results improve, extend and generalize many recently announced results in the current literature.