Global asymptotic stability in a class of generalized Putnam equations

It was conjectured that for every integer m⩾3m⩾3 the unique equilibrium c=1c=1 of the generalized Putnam equationxn+1=∑i=0m−2xn−i+xn−m+1xn−mxnxn−1+∑i=2mxn−i,n=0,1,2,…, with positive initial conditions is globally asymptotically stable. In this paper, we prove this conjecture.