On a New Class of Rational Difference Equation zn+1 = azn+bzn−k+(α +β zn−k)/(A+Bzn−k) - Khaliq, Abdul; Hassan, Sk. Sarif (Journal of Applied Nonlinear Dynamics, 2026)
In this article, we will investigate invariant intervals, periodic character, the character of semi cycles and global asymptotic stability of all positive solutions of a nonlinear rational difference equation of order k+1, zn+1 = azn+bzn−k+(α +β zn−k)/(A+Bzn−k), n = 0,1, ..., where the parameters a, b, α,β and A, B and the initial conditions z−k, z−k+1, z−k+2, ..., z0 are arbitrary positive real numbers. We also have studied the global stability of this equation through numerically solved examples and confirm our theoretical discussion through it.