Lyapunov-type inequalities for even order difference equations

In this work, we establish two new Lyapunov-type inequalities for the 2k2k-order difference equation △2kx(n)+(−1)k−1q(n)x(n+1)=0.△2kx(n)+(−1)k−1q(n)x(n+1)=0. Applying our inequalities, we obtain the lower bounds of the eigenvalue for a related eigenvalue problem.