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 problem 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 sequences. Also, we provided a numerical example to demonstratethe implementablity of our proposed iteration technique.  Our results improve, extend and generalize many recently announced results in the current