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    On some new trapezoidal type inequalities for twice (P, q) differentiable convex functions in post-quantum calculus
    (MDPI, 2021) Thanin Sitthiwirattham; Ghulam Murtaza; Muhammad Aamir Ali; Sotiris K. Ntouyas; Muhammad Adeel; Jarunee Soontharanon; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a (p,q)-integral identity involving the second (p,q)-derivative and then we used this result to prove some new trapezoidal type inequalities for twice (p,q)-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors.