In this paper, we prove a new quantum integral equality involving parameter, left and right derivatives. Then, use the newly established some estimates of Ostrowski, midpoint, trapezoidal Simpson’s type inequalities for q-differentiable convex functions. It is also shown that are refinements existing inside literature. Finally, examples applications given to illustrate investigated results.

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired ob...