On Relative Convex Sequences

TL;DR

This paper introduces the concept of relative convex sequences, explores their properties, and derives new inequalities, extending classical convex sequence inequalities and demonstrating their applications.

Contribution

The paper defines relative convex sequences, establishes their fundamental properties, and proves new inequalities related to Lupas and Hermite-Hadamard-Fejér types.

Findings

Established fundamental properties of relative convex sequences

Proved new inequalities of Lupas and Hermite-Hadamard-Fejér type

Showed applications to deriving inequalities for convex sequences

Abstract

In this paper, we introduce the concept of relative convex sequences and establish their fundamental properties, highlighting their similarities to those of convex sequences. Additionally, we prove new inequalities of the Lupas and Hermite-Hadamard-Fej\'er type for relative convex sequences. In certain cases, and as an application, we show how the concept of relative convexity can facilitate the derivation of new inequalities for convex sequences.