Browsing by Author "Jianqiang Xie"

Now showing 1 - 2 of 2
  • Default Image
    Item
    FRACTIONAL HERMITEÐHADAMARD INEQUALITY, SIMPSONÕS AND OSTROWSKIÕS TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS
    (Rocky Mountain Mathematics Consortium, 2023) Jianqiang Xie; Muhammad Aamir Ali; HŸseyin Budak; Michal Fe_kan; Thanin Sitthiwirattham; M.A. Ali; School of Mathematical Sciences, Nanjing Normal University, Nanjing, China; email: mahr.muhammad.aamir@gmail.com
    We consider the convexity with respect to a pair of functions and establish a HermiteÐHadamard type inequality for RiemannÐLiouville fractional integrals. Moreover, we derive some new SimpsonÕs and OstrowskiÕs type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities. © Rocky Mountain Mathematics Consortium.
  • Default Image
    Item
    Some new midpoint and trapezoidal type inequalities in multiplicative calculus with applications
    (University of Nis, 2023) Jianqiang Xie; Muhammad Aamir Ali; Thanin Sitthiwirattham; M.A. Ali; School of Mathematical Sciences, Nanjing Normal University, China; email: mahr.muhammad.aamir@gmail.com
    In this paper, we use multiplicative twice differentiable functions and establish two new multiplicative integral identities. Then, we use convexity for multiplicative twice differentiable functions and establish some new midpoint and trapezoidal type inequalities in the framework of multiplicative calcu-lus. Finally, we give some applications to special means of real numbers to make these inequalities more interesting for the readers. © 2023, University of Nis. All rights reserved.