An Equivalent Condition to the Jensen Inequality for the Generalized Sugeno Integral

J Inequal Appl. 2017;2017(1):285. doi: 10.1186/s13660-017-1561-2. Epub 2017 Nov 14.

Abstract

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given.

Keywords: convex function; generalized Sugeno integral; the Jensen inequality.