Convex sequences of higher order

Abstract

In this paper we study the class of convex sequences of higher order defined using the difference operators and investigate their properties. The notion of the convex sequence of order r ∈N will be extended for r a real number. Some necessary and sufficient conditions such that a real sequence belongs to the class of convex sequences of higher order r ∈R are introduced. Using different types of means we will investigate the convexity of higher order for real sequences.