On a discrete version of Fejér inequality for α-convex sequences without symmetry condition

Abstract

In this study, we introduce the notion of α\alpha -convex sequences which is a generalization of the convexity concept. For this class of sequences, we establish a discrete version of Fejér inequality without imposing any symmetry condition. In our proof, we use a new approach based on the choice of an appropriate sequence, which is the unique solution to a certain second-order difference equation. Moreover, we obtain a refinement of the standard (right) Fejér inequality for convex sequences.

Keywords

• α-convex sequences
• convex sequences
• fejér-type inequalities
• second-order difference equations
• 26d15
• 52a01
• 39a06