论文标题
伪综合的古典不平等现象
Classical inequalities for pseudo-integral
论文作者
论文摘要
在本文中，我们得出了某些经典的不平等现象，即Young's，Hölder's，Minkowski's和Hermite-Hadamard的不平等现象（也称为$ g $ integral）。对于Young的Hölder's，Minkowski的不平等现象，均涵盖了$ p> 1 $的案例，以及$ p <1，\，p \ ne 0 $。此外，就赫米特 - 哈达玛德不平等而言，还证明了细化，并且作为一种特殊情况，已经推导了几何形状 - 含量 - 千古化量不平等的$ g $ analogue。
In this paper, we have derived certain classical inequalities, namely, Young's, Hölder's, Minkowski's and Hermite-Hadamard inequalities for pseudo-integral (also known as $g$-integral). For Young's, Hölder's, Minkowski's inequalities, both the cases $p>1$ as well as $p<1,\,p\ne 0$ have been covered. Moreover, in the case of Hermite-Hadamard inequality, a refinement has also been proved and as a special case, $g$-analogue of geometric-logarithmic-arithmetic inequality has been deduced.
