Sherman, Hermite-Hadamard and Fejér like inequalities for convex sequences and nondecreasing convex functions

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 Petrovic and Giaccardi?s inequalities. As applications, we establish some generalizatons of Fej?r inequality for convex sequences. We also study inequalities of Hermite-Hadamard type. Thus we extend some recent results of Latreuch and Bela?di [8]. In our considerations we use some matrix methods based on column stochastic and doubly stochastic matrices.