The article presents the following result: Let \(Y\) be a closed convex set in a Banach space \(X\) and \(E\), \(F\) two mappings on \(Y\) for which \[ \| E^ h x-F^ k y\|\leq H(\| x-y\|,\| x-E^ h x\|,\| y-F^ k y\|,\| x-F^ k y\|,\| y-E^ h x\|) \] where \(h\), \(k\) are some positive integers, \(H:R_ +^ s\to R_ +\) is non- decreasing in each variable, and \(H(t,2t,t,2t,t)<t\) for each \(t>0\). If the sequence \(x_ n\) converges to \(u\in Y\) where \(x_{2n+1}=(1- t)x_{2n}+tE^ h x_{2n}\), \(x_{2n+2}=(1-t)x_{2n+1}=tF^ k x_{2n+1}\) for some \(t\in(0,1)\) and \(x_ 0\in Y\), then \(u\) is a unique common fixed point of \(E\) and \(F\), and both \(E\) and \(F\) are continuous at \(u\). Unfortunately, there are many misprints in the article.