Author:
Aras-Gazić G.,Pečarić J.,Vukelić A.
Abstract
AbstractBy 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference15 articles.
1. Atkinson, K.E.: An Introduction to Numerical Analysis, 2nd edn. Wiley, New York (1989)
2. Bullen, P.S.: An inequality of N. Levinson. Publ. Elektroteh. Fak. Univ. Beogr., Ser. Mat. Fiz. 412–460, 109–112 (1973)
3. Čuljak, V., Franjić, I., Ghulam, R., Pečarić, J.: Schur-convexity of averages of convex functions. J. Inequal. Appl. 2011, Article ID 581918 (2011)
4. Farwig, R., Zwick, D.: Some divided difference inequalities for n-convex functions. J. Math. Anal. Appl. 108, 430–437 (1985)
5. Jakšetić, J., Pečarić, J., Roqia, G.: On Jensen’s inequality involving averages of convex functions. Sarajevo J. Math. 8(20)(1), 53–68 (2012)