Estimation Bounds for Nonlinear Integral of the Square of Concave Functions

Abstract

Hermite-Hadamard inequality is an important integral inequality in mathematics giving upper and lower bounds for the integral average of convex (concave) functions defined on closed intervals. Sandor’s inequality is the same Hermite-Hadamard inequality but for the square of convex (concave) functions. In this paper, Sandor’s inequality for nonlinear Sugeno integral is proved, i.e. some optimal bounds for the Sugeno integral of the square of concave functions are given. To illustrate the results, some examples with their geometric interpretations are presented.