In this paper, we suggest a new iterative scheme for finding a common element of the set of solutions of a split equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in Hilbert spaces. We show that the iteration converges strongly to a common solution of the considered problems. A numerical example is illustrated to verify the validity of the proposed algorithm. The results obtained in this paper extend and improve some known results in the literature.

In this paper, we design two inertial-type subgradient extragradient algorithms with line-search process for solving the pseudomonotone variational inequality problems (VIPs) and common fixed-point problem (CFPP) of finite Bregman relatively nonexpansive mapping and a Bregman relatively demicontractive mapping in p-uniformly convex and uniformly smooth Banach spaces, which are more general than Hilbert spaces. Under mild conditions, we derive weak and strong convergence of the suggested algorithms to a common solution of the VIPs and CFPP, respectively. Additionally, an illustrated example is furnished to back up the feasibility and implementability of our proposed methods.