Convergence theorems to common fixed points for infinite families of nonexpansive mappings in strictly convex Banach spaces (Q1433475)

The author proves convergence theorems to common fixed points for infinite families of nonexpansive mappings in strictly convex Banach spaces. One of the results is the following: Let \(C\) be a compact convex subset of a strictly convex Banach space \(E\). Let \(\{T_n:n\in \mathbb{N}\}\) be a sequence of nonexpansive mappings on \(C\) with \(\bigcap^\infty_{n=1} F(T_n)\neq\emptyset\). Let \(\{\lambda_n\}\) be a sequence of positive numbers such that \(\sum^\infty_{n=1} \lambda_n< 1\). Define a sequence \(\{x_n\}\) in \(C\) by \(x_1\in C\) and \[ x_{n+1}= \Biggl(1- \sum^n_{i=1} \lambda_i\Biggr) x_n+ \sum^n_{i=1} \lambda_i T_i x_n \] for \(n\in\mathbb{N}\). Then \(\{x_n\}\) converges strongly to a common fixed point of \(\{T_n:n\in \mathbb{N}\}\).