On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus

Abstract

Abstract In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature.