The main objective of this article is to establish a new post quantum version of Montgomery identity. Some estimates of associated post quantum bounds are also obtained. In order to obtain the main results of the article, we use the preinvexity property of the functions. Some special cases are also discussed in detail. Finally, we present some applications of the obtained results, which shows the significance of the discussed results.

中文翻译：

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\（（\ mathrm {p}，\ mathrm {q}）\） -蒙哥马利身份分析和\（（\ mathrm {p}，\ mathrm {q}）\）边界估计与应用

本文的主要目的是建立蒙哥马利身份的新的后量子版本。还获得了相关的后量子界的一些估计。为了获得本文的主要结果，我们使用了函数的preinvexity属性。还详细讨论了一些特殊情况。最后，我们介绍了所得结果的一些应用，这表明了所讨论结果的重要性。