ABSTRACT
Please recall our classification convention in which all parameters that appear in these equations are positive, the initial conditions are nonnegative, and the denominators are always positive.
Two of these equations, namely Eqs(4.1) and (4.4) are Riccati-type difference equations. (See Section 1.6 in the Preliminary Results). Also Eqs(4.2) and (4.8) are essentially Riccati equations. Indeed if {xn} is a solution of Eq(4.2), then the subsequences {x2n−1} and {x2n} satisfy the Riccati equation of the form of Eq(4.1). Similarly, if {xn} is a solution of Eq(4.8), then the subsequences {x2n−1} and {x2n} satisfy the Riccati equation
yn+1 = γyn
A+ Cyn n = 0, 1, . . . .
