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

Now showing 1 - 2 of 2
  • Default Image
    Item
    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.
  • Default Image
    Item
    On some new inequalities of hermiteÐhadamard midpoint and trapezoid type for preinvex functions in (P, q)-calculus
    (MDPI, 2021) Ifra Bashir Sial; Muhammad Aamir Ali; Ghulam Murtaza; Sotiris K. Ntouyas; 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 paper, we establish some new HermiteÐHadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for (p, q)-differentiable preinvex functions in the context of (p, q)-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature 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. Licensee MDPI, Basel, Switzerland.