Affiliation:
1. Department of Mathematics , South Asian University , Akbar Bhawan, Chanakya Pur i, New Delhi - 110021 , India
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.