On the refinements of the Jensen-Steffensen inequality

Abstract

Abstract In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied. 2010 Mathematics Subject Classification. 26D15.

Keywords

• Jensen-Steffensen inequality
• refinements
• exponential and logarithmic convexity
• mean value theorems