Common fixed points of two pairs of weakly commuting mappings


Brian Fisher, Salvatore Sessa




A common fixed point theorem is proved involving two pairs of weakly commuting mappings on a metric space $(X,d)$ satisfying \[ d(Sx,Ty)eq g(d(Ix,Jy),d(Ix,Sx),d(Jy,Ty)) \] for all $x,y$ i $X$ where $g\colon[0,\infty)^3\to[0,\infty)$ satisfies (i) $g(1,1,1)=h<1$ and (ii) if $u,v\geq0$ and either $u\leq g(u,v,v)$ or $u\leq g(v,u,v)$ or $u\leq g(v,v,u)$, then $u\leq hv$.