Some new post‐quantum integral inequalities involving multi‐parameter and their applications. (18th February 2022)

• Record Type: Journal Article
• Authors: Raees, Muhammad; Kashuri, Artion; Awan, Muhammad Uzair; Anwar, Matloob
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 10(2022)
• Page Start: 5965
• Page End: 5987
• Publication Date: 2022-02-18
• Subjects: Hermite–Hadamard inequality -- Simpson inequality -- n‐polynomial convex function -- post‐quantum calculus -- Hölder inequality -- Lipschitz function -- special means; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8151
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we establish a generic identity for ( p, q )‐differentiable functions involving multi‐parameter. Using this identity as an auxiliary result, we derive some new post‐quantum fundamental integral inequalities, including Simpson‐type and Hermite–Hadamard‐type pertaining n ‐polynomial convex functions. Also, by considering the boundedness and the Lipschitz condition of ( p, q )‐differentiable functions further results are given. Finally, in order to show the significance of our results, we present two illustrative examples and some applications to special means for different positive real numbers.