On the rational difference equation yn+1 = α0yn+α1yn−p+α2yn−q+α3yn−r+α4yn−s / β0yn+β1yn−p+β2yn−q+β3yn−r+β4yn−s

In this paper, we examine and explore the boundedness, periodicity, and global stability of the positive solutions of the rational difference equation yn+1 = α0yn+α1yn−p+α2yn−q+α3yn−r+α4yn−s / β0yn+β1yn−p+β2yn−q+β3yn−r+β4yn−s where the coefficients αi, βi ∈ (0, ∞) , i = 0, 1, 2, 3, 4, and p, q, r, and s are positive integers. The initial conditions y−s,. . . ,y−r,. . . , y-q,. . . , y-p,. . . ,y−1,y0 are arbitrary positive real numbers such that p q r s. Some numerical examples will be given to llustrate our result.