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In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of infinite family of asymptotically quasi-ϕ-nonexpansive mappings and of the set of solutions for finite equilibrium problems in a real Banach space. Our results are the generalization of the results (Shehu in Comput. Math. Appl. 63:1089-1103, 2012; Kim in Fixed Point Theory Appl., 2011, doi:10.1186/1687-1812-2011-10) and (Kim and Buong in Fixed Point Theory Appl., 2011, doi:10.1155/2011/780764), and improvement of the result (Yang et al. in Appl. Math. Comput. 218:6072-6082, 2012).

fixed point theory and applications

Strong convergence theorems for fixed point problems of infinite family of asymptotically quasi-ϕ-nonexpansive mappings and a system of equilibrium problems