On a fixed point theorem of Greguš

We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e. ‖TIx−ITx‖≤‖Ix−Tx‖   for   any   x   in   X, and satisfy the inequality ‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖} for all x, y in C, where 0