Classical inequalities for (p, q)-calculus on finite intervals

In this paper, certain classical inequalities, namely, trapezoidal inequality (first as well as second order), generalized weighted Hölder’s inequality, Minkowski’s inequality and Grüss type inequalities have been investigated in the framework of (p, q)-calculus. These inequalities extend the corresponding known inequalities in q-calculus. Moreover, in the case of trapezoidal inequality, we improve upon the constant as well. To prove (p, q)-Grüss inequalities, we first derive (p, q)-Andreief’s identity which, in particular, contains (p, q)-Korkine identity.