On new generalized quantum integrals and related Hermite-Hadamard inequalities

In this article, we introduce a new concept of quantum integrals which is called $^{\kappa_{2}}T_{q}$-integral. Then we prove several properties of this concept of quantum integrals. Moreover, we present several Hermite-Hadamard type inequalities for $^{\kappa_{2}}T_{q}$-integral by utilizing differentiable convex functions. The results presented in this article are unification and generalization of the comparable results in the literature.