Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations

Abstract EN

The classical Hölder inequality shows an interesting upper bound for Lebesgue integral of the product of two functions.

This paper proposes Hölder type inequalities and reverse Hölder type inequalities for Sugeno integrals under usual multiplication operations for nonincreasing concave or convex functions.

One of the interesting results is that the inequality, (S)∫01f(x)pdμ1/p(S)∫01g(x)qdμ1/q≤p-q/p-p-q+1∨q-p/q-q-p+1(S)∫01f(x)g(x)dμ, where 1

As a special case, we consider Cauchy-Schwarz type inequalities for Sugeno integrals involving nonincreasing concave or convex functions.

Some examples are provided to illustrate the validity of the proposed inequalities.