Luangboon, WaewtaNonlaopon, KamsingTariboon, JessadaNtouyas, Sotiris K.Budak, Hüseyin2023-07-262023-07-2620222227-7390https://doi.org/10.3390/math10050826https://hdl.handle.net/20.500.12684/12613In this paper, we establish a new (p,q)(b)-integral identity involving the first-order (p,q)(b)-derivative. Then, we use this result to prove some new (p,q)(b)-integral inequalities related to Hermite-Hadamard inequalities for (p,q)(b)-differentiable convex functions. Furthermore, our main results are used to study some special cases of various integral inequalities. The newly presented results are proven to be generalizations of some integral inequalities of already published results. Finally, some examples are given to illustrate the investigated results.en10.3390/math10050826info:eu-repo/semantics/openAccessHermite-Hadamard Inequality; Convex Function; (P.Q)-Differentiable Function; (P.Q)-Integral Inequalities; (P.Q)-CalculusMidpoint-Type Inequalities; Quantum; SimpsonArticle1052-s2.0-85126334884WOS:000773824600001Q2Q1