Lyapunov-type inequalities for even order difference equations

In this work, we establish two new Lyapunov-type inequalities for the 2 k -order difference equation △ 2 k x ( n ) + ( − 1 ) k − 1 q ( n ) x ( n + 1 ) = 0 . Applying our inequalities, we obtain the lower bounds of the eigenvalue for a related eigenvalue problem.