A note on common fixed point theorems (Q1068381)

Banach's contracting mapping theorem is generalized to a theorem guaranteeing that under some conditions two mappings S, T of a complete metric space into itself have a common fixed point. This point can be calculated as a limit of a sequence, obtained by applying T and S (in proper order) to an arbitrary point \(x_ 0\). Existing generalizations of the Banach theorem [\textit{A. Meir} and \textit{E. Keeler}, ibid. 28, 326-329 (1969; Zbl 0194.449) and \textit{M. A. Geraghty}, ibid. 48, 811-817 (1974; Zbl 0308.54033) and some others] turn out to be special versions of this general common fixed point theorem (or of one of its corollaries).