Let be a Banach space and a subset of . Let . is called -nonexpansive on if for all . The set of fixed points of (resp. ) is denoted by (resp. ). The set is called the set of best approximants to from .
In the case that and are commuting () on , G. Jungck and S. Sessa [Math. Jap. 42, No. 2, 249–252 (1995; Zbl 0834.54026)] proved that, under certain conditions, . Later, N. Shahzad [Tamkang J. Math. 32, No. 1, 51–53 (2001; Zbl 0978.41020)] extended this result to a class of noncommuting maps. In this paper it is proved the validity of this result for generalized -nonexpansive maps.