Global asymptotic stability in a class of Putnam-type equations Original Research Article

In this paper, we initiate the study of a class of Putnam-type equation of the form View the MathML sourcexn+1=A1xn+A2xn-1+A3xn-2xn-3+A4B1xnxn-1+B2xn-2+B3xn-3+B4,n=0,1,2,…, Turn MathJax on where A1A1, A2A2, A3A3, A4A4, B1B1, B2B2, B3B3, B4B4 are positive constants with A1+A2+A3+A4=B1+B2+B3+B4A1+A2+A3+A4=B1+B2+B3+B4, x-3x-3, x-2x-2, x-1x-1, x0x0 are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c=1c=1 of such equations.