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In this investigation, for convex functions, some new (p , q) –Hermite–Hadamard-type inequalities using the notions of (p , q) π 2 derivative and (p , q) π 2 integral are obtained. Furthermore, for (p , q) π 2 -differentiable convex functions, some new ( p , q ) estimates for midpoint and trapezoidal-type inequalities using the notions of (p , q) π 2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1 − can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities. [ABSTRACT FROM AUTHOR]