Some new q-Hermite-Hadamard-Mercer inequalities and related estimates in quantum calculus

Abstract

In this paper, we establish a quantum version of the Hermite-Hadamard-Mercer inequalities using the well-known Jensen-Mercer inequality. Moreover, we derive some new q-midpoint and q-trapezoidal type inequalities for differentiable functions. The newly developed inequalities are also shown to be the extensions of preexisting inequalities in the literature.