In this paper, we prove Sherman like inequalities for convex sequences and nondecreasing convex functions. Thus we develop some results by S. Wu and L. Debnath [19]. In consequence, we derive discrete versions for convex sequences of Petrović and Giaccardi's inequalities. As applications, we establish some generalizatons of Fejér inequality for convex sequences. We also study inequalities of Hermite-Hadamard type. Thus we extend some recent results of Latreuch and Belaïdi [8]. In our considerations we use some matrix methods based on column stochastic and doubly stochastic matrices.