Sherman, Hermite-Hadamard and Fej´er like Inequalities for Convex Sequences and Nondecreasing Convex Functions

Abstract

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 \cite{WD}.
In consequence, we derive discrete versions for convex sequences of
Petrovic and Giaccardi's inequalities.
As applications, we establish some generalizatons
of Fejer inequality for convex sequences.
We also study inequalities of Hermite-Hadamard type.
Thus we extend some recent results of Latreuch and Belaidi \cite{LB1}.
In our considerations we use some matrix methods
based on column stochastic and doubly stochastic matrices.