Hyers-Ulam Stability of Hyperbolic Mobius Difference Equation

Hyers-Ulam stability of the difference equation with the initial point z(0) as follows z(i+1) = az(i)+b/cz(i) + d is investigated for complex numbers a, b, c and d where ad - bc = 1, c not equal 0 and a + d is an element of R \ [-2, 2]. The stability of the sequence {z(n)}(n is an element of N0) holds if the initial point is in the exterior of a certain disk of which center is - d/c. Furthermore, the region for stability can be extended to the complement of some neighborhood of the line segment between - d/c and the repelling fixed point of the map z bar right arrow az+b/cz+d . This result is the generalization of Hyers-Ulam stability of Pielou logistic equation.