In this paper, we first consider an iteration scheme given by an infinite family of nonexpansive mappings in Banach spaces and then prove a strong convergence theorem for the family of nonexpansive mappings. Using this result, we consider the feasibility problem of finding a solution of infinite convex inequalities and the problem of finding a common fixed point of infinite nonexpansive mappings.
"STRONG CONVERGENCE TO COMMON FIXED POINTS OF INFINITE NONEXPANSIVE MAPPINGS AND APPLICATIONS." Taiwanese J. Math. 5 (2) 387 - 404, 2001. https://doi.org/10.11650/twjm/1500407345