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The primary goal of this paper is to present and study an inertial projection algorithm for solving the split best proximity and mixed equilibrium problems. We find a solution of the best proximity problem in such a way that its image under a bounded linear operator is the solution of the mixed equilibrium problem under the setting of real Hilbert spaces. We construct an iterative algorithm for the proposed problem and prove a weak convergence theorem. Moreover, we deduce some consequences from the main convergence result. Finally, a numerical experiment is presented to demonstrate the convergence analysis of our algorithm. The methodology and results presented in this work improve and unify some previously published findings in this field. [ABSTRACT FROM AUTHOR]

Combining inertial-type methods with projection extragradient methods, we propose three inertial extragradient algorithms for solving nonmonotone and non-Lipschitzian equilibrium problems in Hilbert spaces. Under the assumption that the solution set of the associated Minty equilibrium problem is nonempty, we establish the weak and strong convergence of the proposed algorithms, respectively. The convergence is guaranteed without any monotonicity and Lipschitz-type continuity of the equilibrium bifunction. Some numerical experiments illustrate that the presented algorithms are faster than the existing projection extragradient ones. [ABSTRACT FROM AUTHOR]