In the present study, two new classes of convex functions are established with the aid of Raina’s function, which is known as the ψ - s -convex and ψ -quasi-convex functions. As a result, some refinements of the Hermite–Hadamard ( ℋℋ {\mathcal{ {\mathcal H} {\mathcal H} }} )-type inequalities regarding our proposed technique are derived via generalized ψ -quasi-convex and generalized ψ - s -convex functions. Considering an identity, several new inequalities connected to the ℋℋ {\mathcal{ {\mathcal H} {\mathcal H} }} type for twice differentiable functions for the aforesaid classes are derived. The consequences elaborated here, being very broad, are figured out to be dedicated to recapturing some known results. Appropriate links of the numerous outcomes apprehended here with those connecting comparatively with classical quasi-convex functions are also specified. Finally, the proposed study also allows the description of a process analogous to the initial and final condition description used by quantum mechanics and special relativity theory.

中文翻译：

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几类新的广义ψ-凸函数的新量子积分不等式及其在物理系统中的范围

在本研究中，借助于Raina函数建立了两类新的凸函数，分别称为ψ-s-凸函数和ψ-拟凸函数。结果，通过广义ψ-拟凸和广义ψ- s-凸函数。考虑到同一性，对于上述类的两个可微分函数，得出了与new {\ mathcal {{\ mathcal H} {\ mathcal H}}}类型有关的几个新不等式。此处阐述的后果非常广泛，已被认为专门用于重新获得某些已知结果。还指出了这里所理解的众多结果与那些与经典准凸函数相对连接的结果之间的适当联系。最后，提出的研究还允许描述类似于量子力学和狭义相对论所使用的初始和最终条件描述的过程。