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This paper provides iterative construction of a common solution associated with a class of equilibrium problems and split convex feasibility problems. In particular, we are interested in the equilibrium problems defined with respect to the pseudomonotone and Lipschitz-type continuous equilibrium problem together with the generalized split null point problems in real Hilbert spaces. We propose an iterative algorithm that combines the hybrid extragradient method with the inertial acceleration method. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under suitable set of constraints and numerical results concerning the viability of the proposed algorithm with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We consider a general setting in which the involved sets are represented as level sets of given convex functions, and propose a constructible linear approximation scheme that involves the subgradient of the associated convex functions. Strong convergence of the proposed scheme is established under mild assumptions and several synthetic and practical numerical illustrations demonstrate the validity and advantages of our method compared with related schemes in the literature. [ABSTRACT FROM AUTHOR]