Berwald-type inequalities for Sugeno integral with respect to ( α , m , r ) g ${ ( {\alpha,m,r} )_{g}}$ -concave functions

Abstract

Abstract In this paper, we introduce the concept of an ( α , m , r ) g ${ ( {\alpha,m,r} )_{g}}$ -concave function as a generalization of a concave function. Then we establish Berwald-type inequalities for the Sugeno integral based on this kind of functions. Our work generalizes the previous results in the literature. Finally, we give some conclusions and problems for further investigations.

Keywords

• Berwald-type inequality
• Sugeno integral
• ( α , m , r ) g $( {\alpha,m,r} )_{g}$ -concave function