On a fixed point theorem of Greguš
Brian Fisher, Salvatore Sessa · International Journal of Mathematics and Mathematical Sciences · 1986
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. urn:x-wiley:01611712:media:ijmm191262:ijmm191262-math-0001 and satisfy the inequality urn:x-wiley:01611712:media:ijmm191262:ijmm191262-math-0002 for all x, y in C, where 0 < a < 1. It is proved that if I is linear and non‐expansive in C and such that IC contains TC, then T and I have a unique common fixed point in C.