On sequences satisfying fourth-order difference inequalities

We consider the class of sequences a = (a 1 , ,a n ) R n satisfying the fourth-order difference inequality 4 a i 0 , i = 1, ,n -4 .A Hermite-Hadamard-type inequality is established for this class of sequences.The proof of our result is based on the choice of an appropriate sequence which is the solution to a certain fourth-order difference equation.Moreover, if a is a convex sequence, we obtain an interesting refinement of the right discrete Hermite-Hadamard inequality.We next extend our study to the class of matrices satisfying a system of fourth-order difference inequalities.In particular, we obtain a trace inequality for the class of symmetric matrices.