# Common Fixed Points for Countable Families of Nonexpansive Mappings

Various authors have studied iterative schemes similar to that of Bauschke (Theorem BSK, Chapter 15) in more general Banach spaces on one hand and using various conditions on the sequence {λ_{n}} on the other hand (see, for example, Colao *et al*. [192], Yao [532], Takahashi and Takahashi [482], Plubtieng and Punpaeng [385], Ceng *et al*. [193], Chidume and Ali [125], Jung [264], Jung *et al*. [265], O'Hara *et al*. [361], Zhou *et al*. [559]). Most of the results in these references are proved for *finite* families of nonexpansive mappings defined in Hilbert spaces.

Convergence theorems have also been proved for common fixed points of countable *infinite* families of nonexpansive mappings. Before we proceed, we first state the following important theorem.

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