Classical inequalities for pseudo-integral

Abstract

Abstract In this paper, we have derived certain classical inequalities, namely Young’s, Hölder’s, Minkowski’s and the Hermite–Hadamard inequalities for a pseudo-integral (also known as g-integral). For Young’s, Hölder’s and Minkowski’s inequalities, the cases p > 1 {p>1} and p < 1 {p<1} , p ≠ 0 {p\neq 0} , have been covered. Moreover, in the case of the Hermite–Hadamard inequality, the refinement has also been proved and, as a special case, a g-analogue of a geometric-logarithmic-arithmetic inequality has been deduced.