Sherman, Hermite-Hadamard and Fejér 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 [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.

On convex and concave sequences and their applications

“…The investigation of convex sequences probably started in the book Mitrinović [4]. This subfield is still very active, some recent results and applications have been obtained by Krasniqi [2], Niezgoda [8][9][10], Sofonoea-Ţincu-Acu [13], Tabor-Tabor-Żoldak [14], Wu-Debnath [15], Yıldız [16]. In this paper we introduce the notions of q-convex, q-affine and q-concave sequences and we present some basic results on them and we establish their surprising connection to Chebyshev polynomials of the first and of the second kind.…”