Quantum Hermite–Hadamard inequality by means of a Green function

Abstract

The purpose of this work is to present the quantum Hermite-Hadamard inequality through the Green function approach. While doing this, we deduce some novel quantum identities. Using these identities, we establish some new inequalities in this direction. We contemplate the possibility of expanding the method, outlined herein, to recast the proofs of some known inequalities in the literature.

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“…19 Recently, Alp et al 20 obtained quantum estimations for q-midpoint and q-Hermite-Hadamard inequalities. q-Integral inequalities have been studied extensively by several researchers either in classical analysis or in the quantum one; see previous studies [20][21][22] and references cited therein.…”