This paper is concerned with de Marr’s result on the existence of a common fixed point for an arbitrary family of symmetric Banach operator pairs in hyperconvex metric spaces without assuming compactness [R. DeMarr
, Pac. J. Math. 13, 1139–1141 (1963; Zbl 0191.14901
)]. It is based on the very recent work of J.-R. Chen
and Z.-K. Li
[Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 10, 3086–3090 (2011; Zbl 05895597
)]. Necessary and sufficient conditions for an invertible semigroup of isometric mappings in hyperconvex metric spaces to have a common fixed point are given. Moreover, some results on invariant approximations for Banach operator pairs in hyperconvex metric spaces are also discussed.