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The <i>q</i>-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving <i>q</i>-symmetric integrals are used to extend some Ostrowski-type inequalities. The <i>q</i>-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or <i>s</i>-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for <i>s</i>-convex functions are also acquired with the help of <i>q</i>-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.