Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral

Abstract

In this investigation, for convex functions, some new (p,q)–Hermite–Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus

“…Similarly, we can compute the second integral by using the Definition 10, for more details see in [18].…”

“…Furthermore, Noor et al [6], Sudsutad et al [7], and Zhuang et al [8] played an active role in the study and some integral inequalities have been established which give quantum analog for the right part of Hermite-Hadamard inequality by using q-differentiable convex and quasi-convex functions. Numerous mathematicians have carried out research in the area of q-calculus analysis; interested readers may check the works in [9][10][11][12][13][14][15][16][17][18][19].…”

Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus

“…Tunç and E. Göv [23] presented the (p, q)-derivative and (p, q)-integral on finite intervals in 2016, proved some of their properties, and proved a number of integral inequalities using the (p, q)-calculus. Many researchers have recently begun working in this direction, based on the works of M. Tunç and E. Göv, and some further findings on the analysis of (p, q)-calculus can be found in [24][25][26][27].…”

Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

“…To prove Ostrowski's inequalities, Chu et al [18] used the concepts of the b D p,q -difference operator and (p, q) b -integral. Recently, Vivas-Cortez et al [38] generalized the results of [15] and proved HH type inequalities and their left estimates using the b D p,q -difference operator and (p, q) b -integral.…”