New post quantum analogues of Ostrowski-type inequalities using new definitions of left–right $(p,q)$-derivatives and definite integrals
Yu‐Ming Chu, Muhammad Uzair Awan, Sadia Talib, Muhammad Aslam Noor, Khalida Inayat Noor
Abstract
Abstract The main objective of this paper is to introduce a new more elegant notion of left–right $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -derivative and definite integrals. To show the significance of these concepts, we discuss some of their basic properties. A new generalized $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -integral identity is also obtained. Utilizing this identity as an auxiliary result we then obtain our main results using the concept of n -polynomial convex functions.