Let $ C_D, A_D, J_D $ denote the smallest constants involved in the stability of convexity, affinity and of the Jensen equation of functions defined on a convex subset D of $ {\Bbb R}^n $ . By a theorem of J. W. Green, $ C_D \le c\cdot \log (n+1) $ for every convex $ D\subset {\Bbb R}^n $ , where c is an absolute constant. We prove that the lower estimate $ C_D \ge c\cdot \log (n+1) $ is also true, supposing that int $ D \neq {\not 0} $ .¶We show that $ A_D \le 2 C_D $ and $ A_D \le J_D \le 2A_D $ for every convex $ D\subset {\Bbb R}^n $ . The constant $ J_D $ is not always of the same order of magnitude as $ C_D $ ; for example $ J_D = 1 $ if $ D ={\Bbb R}^n $ . We prove that there are convex sets (e.g. the n-dimensional simplex) with $ J_D \ge c\cdot \log n $ .