Abstract
In this research article, we introduce a novel iterative approach that builds upon a two-step extragradient-viscosity method. This method aims to find a common element among the solution set of a variational inequality, an equilibrium problem, and the set of common fixed points from a countable family of demicontractive mappings in a Hilbert space. We offer a robust convergence theorem for the proposed iterative scheme, considering certain well-conditioned parameters. Our findings represent an improvement over similar results already available in the existing literature. Furthermore, we demonstrate the applicability of our main result to W-mappings. Lastly, we present two numerical examples to exhibit the consistency and accuracy of our devised scheme.
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