Inequalities for convex sequences and nondecreasing convex functions

Abstract

In this paper, by using Wu–Debnath’s method, we establish inequalities of Hammer–Bullen type for convex sequences and nondecreasing convex functions. In particular, we give an extension of a recent Farissi’s inequality. By assuming the symmetry of an involved sequence, we derive an inequality of Fejer–Hammer–Bullen type for convex sequences. In addition, we establish some companions of an Hermite–Hadamard like inequality by Latreuch and Belaidi. In our approach we use matrix methods based on column stochastic matrices.