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The aim of this paper is to prove a counterpart of the Banach fixed point principle for mappings f : l∞(X) → X, where X is a metric space and l∞(X) is the space of all bounded sequences of elements from X. Our result generalizes the theorem obtained by Miculescu and Mihail in 2008, who proved a counterpart of the Banach principle for mappings f : X → X, where X is the Cartesian product of m copies of X. We also compare our result with a recent one due to Secelean, who obtained a weaker assertion under less restrictive assumptions. We illustrate our result with several examples and give an application.

A fixed point theorem for mappings on the l∞-sum of a metric space and its application