Browsing by Subject "(p, q)-calculus"

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    Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions
    (MDPI, 2022) Thanin Sitthiwirattham; Ghulam Murtaza; Muhammad Aamir Ali; Chanon Promsakon; Ifra Bashir Sial; Praveen Agarwal; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com
    In this study, first we establish a (p, q)-integral identity involving the second (p, q)-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-(p, q)-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.