MMN-4997
New quantum boundaries for q-trapezoidal and q-midpoint types inequalities for (η_1,η_2)-convex functions
Humaira Kalsoom; Zareen A. Khan;Abstract
The primary emphasis of your study lies in elucidating the advancements made in the bounds of q-Hermite–Hadamard inequality and their pragmatic implications in the field of Quantum Calculus. The research initiates by deducing two quantum integral (q-integral) identities, employing quantum derivatives and integrals. Subsequently, novel q-midpoint and q-trapezoidal approximations are introduced for the recently developed q-Hermite-Hadamard inequality. This inequality, as established by Bermudo et al., encompasses left and right integrals and is applicable to q-differentiable $(\eta_1,\eta_2)$-convex functions. To substantiate the efficacy and accuracy of the newly devised quantum inequalities, illustrative examples are provided, encapsulating the practical utility of your research.
Vol. 26 (2025), No. 2, pp. 877-896