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We use two parameters for functions whose second (<i>q</i>, <i>ω</i>)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on (<i>q</i>, <i>ω</i>)-Hahn difference operator. Furthermore, we procure some <i>q</i>-integral and continuous inequalities as special cases of the main results as well these generalizations. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.