Abstract
In this article, we propose and investigate several iterative methods for approximating fixed points of a firmly nonexpansive-type mapping and for finding a common element of the set of fixed points of the firmly nonexpansive-type mapping and the set of solutions of an equilibrium problem in Banach space. By using the conception of generalized projection, strong convergence theorems for firmly nonexpansive-type mappings and equilibrium problems in Banach space are established under suitable assumptions, which extend and modify some known results in the literature.
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