New Quantum Estimates for Midpoint and Trapezoid Type Inequalities Through (α,m)-Convex Functions with Applications - Gulshan, Ghazala; Aamir Ali, Muhammad; Budak, Hüseyin; Hussain, Rashida (Annals of Mathematics and Physics, 2024)
The main goal of current investigation is to present two new q-integral identities for midpoint and trapezoid type inequalities. Then using these identities, we develop several new quantum estimates for midpoint and trapezoid type inequalities via (α, m)-convexity. Some special cases of these new inequalities can be turned into quantum midpoint and quantum trapezoid type inequalities for convex functions, classical midpoint and trapezoid type inequalities for convex functions without having to prove each one separately. Finally, we discuss how the special means can be used to address newly discovered inequalities. 2010 Mathematics Subject Classification. 26D10, 26D15, 26B25.