In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called -polynomial preinvex functions. We use the -polynomial preinvex functions to develop -analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for -differentiable function. However, the problem has been proven to utilize the obtained identity, we give -analogues of the Ostrowski-type integrals inequalities which are connected with the -polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.

中文翻译：

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一类函数的多项式凸性内-Ostrowski型不等式的新估计

在本文中，我们开发了一个新颖的框架来研究依赖于任意非负函数的一类新的preinvex函数，这称为-多项式preinvex函数。我们使用-多项式preinvex函数来开发-坐标上Ostrowski型积分不等式的类似物。通过系统的方法研究了量子微积分激发的不同特征和性质。我们通过推断为一个新的身份讨论有关的Ostrowski型的量子不平等的建议和不同的结果-微函数。但是，事实证明该问题可以利用所获得的身份，我们给出-Ostrowski型积分不等式的类似物，它们与-多项式preinvex函数有关。我们的结果是先前论文中结果的概括。