A Global Convergence Result for a Higher Order Difference Equation.

The article presents a study on the result of a global convergence for a higher order difference equation. It is noted that the function ƒ in the equation does not need to be monotonous in each variable, and the condition ƒ (x,....,x) ≤ x can be omitted as an irrelevant one. It is assumed that (xn) is a solution of the difference equation, for which there is an n0 ∈ ℕ. It is concluded that any function ƒ from the previously described class of functions satisfies the conditions from Theorem 1.4.