In this paper, quantum version of Montgomery identity by applying $q^{b}$-integral is obtained. By employing the established identity, some new quantum Ostrowski type inequalities are proved. Several special cases of our main results are presented. It is also shown that the results presented in this paper generalize several other well known inequalities given in the existing literature on this subject.

In this research, we offer two new quantum integral equalities for recently defined $q^{b}$-integral and derivative, the derived equalities then used to prove quantum integral inequalities of Simpson’s and Newton’s type for preinvex functions. We also considered the special cases of established results and offer several new and existing results inside the literature of Simpson’s and Newton’s type inequalities.