An equivalent condition to the Jensen inequality for the generalized Sugeno integral

Mohsen Jaddi; Ali Ebadian; Manuel de la Sen; Sadegh Abbaszadeh

doi:10.1186/s13660-017-1561-2

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.

Authors

Mohsen Jaddi¹, Ali Ebadian¹, Manuel de la Sen², Sadegh Abbaszadeh¹

Affiliations

¹ Department of Mathematics, Payame Noor University, Tehran, 19395-4697 Iran.
² Department of Electricity and Electronics, University of the Basque Country, Bilbao, 466, 48080 Spain.

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.