New Quantum Estimates for Midpoint and Trapezoid Type Inequalities Through (α,m)-Convex Functions with Applications

Ghazala Gulshan, Muhammad Aamir Ali, Hüseyin Budak* and Rashida Hussain

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.

Keywords:

Published on: Aug 6, 2024 Pages: 222-231

Full Text PDF Full Text HTML DOI: 10.17352/amp.000126
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