Browsing by Author "Xue-Xiao You"

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    On some new Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in (p, q)-calculus with applications
    (De Gruyter Open Ltd, 2022) Xue-Xiao You; Muhammad Aamir Ali; Humaira Kalsoom; Jarunee Soontharanon; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for Nslscs, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this study, we establish some new Hermite-Hadamard type inequalities for s-convex functions in the second sense using the post-quantum calculus. Moreover, we prove a new (p, q)\left(p,q)-integral identity to prove some new Ostrowski type inequalities for (p, q)\left(p,q)-differentiable functions. We also show that the newly discovered results are generalizations of comparable results in the literature. Finally, we give application to special means of real numbers using the newly proved inequalities. © 2022 Xue-Xiao You et al., published by De Gruyter.
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    Post-quantum simpsonÕs type inequalities for coordinated convex functions
    (American Institute of Mathematical Sciences, 2022) Xue-Xiao You; Muhammad Aamir Ali; Ghulam Murtaza; Saowaluck Chasreechai; Sotiris K. Ntouyas; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we prove some new SimpsonÕs type inequalities for partial (p, q)-differentiable convex functions of two variables in the context of (p, q)-calculus. We also show that the findings in this paper are generalizations of comparable findings in the literature. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).