On Fejér Type Inequalities via (p,q)-Calculus

Abstract

In this paper, we use (p,q)-integral to establish some Feje´r type inequalities. In particular, we generalize and correct existing results of quantum Feje´r type inequalities by using new techniques and showing some problematic parts of those results. Most of the inequalities presented in this paper are significant extensions of results which appear in existing literatures.

Post quantum Ostrowski‐type inequalities for coordinated convex functions

“…In 2016, Tunç and Göv 25,26 introduced the $$$ \left(p,q\right) $$$‐derivative and $$$ \left(p,q\right) $$$‐integral on finite intervals, proved some of its properties and gave many integral inequalities by using $$$ \left(p,q\right) $$$‐calculus. Recently, according to works of Tunç and Göv, many researchers started working in this direction, some more results about $$$ \left(p,q\right) $$$‐calculus are in previous works 27–33 . It is worth to note here that $$$ \left(p,q\right) $$$ calculus cannot be derived directly by replacing $$$ q $$$ by $$$ q/p $$$ in $$$ q $$$ calculus, but $$$ q $$$ calculus can be retaken by setting $$$ p=1 $$$ in $$$ \left(p,q\right) $$$ calculus.…”

“…Recently, according to works of Tunç and Göv, many researchers started working in this direction, some more results about (p, q)-calculus are in previous works. [27][28][29][30][31][32][33] It is worth to note here that (p, q) calculus cannot be derived directly by replacing q by q∕p in q calculus, but q calculus can be retaken by setting p = 1 in (p, q) calculus.…”

On Hermite–Hadamard–Fejér-Type Inequalities for η-Convex Functions via Quantum Calculus

“…Recently, there have been many works about quantum integral inequalities, especially quantum Hermite-Hadamard-Fejér-type inequalities. Interested readers can see [13][14][15][16][17][18] and the references therein.…”