On generalization of Levinson’s inequality involving averages of 3-convex functions

Abstract

Abstract By using an integral arithmetic mean, a generalization of Levinson’s inequality given in (Pečarić et al. in Convex Functions, Partial Orderings, and Statistical Applications. Mathematics in Science and Engineering, vol. 187, 1992) and results from (Vukelić in Appl. Anal. Discrete Math. 14:670–684, 2020), we give extension of Wulbert’s result from (Wulbert in Math. Comput. Model. 37:1383–1391, 2003). Also, we obtain inequalities with divided differences for the functions of higher order.

Keywords

• Levinson’s inequality
• n-convex function
• ( n , m ) $(n,m)$ -convex function
• Divided differences