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The well-known Hermite-Hadamard inequality for convex functions is extensively studied for different kinds of integrals and derivatives. This paper investigates some of its variants for q − h -integrals using properties of convex functions. Inequalities for q -integrals that have been published in recent years can be extracted from the main results of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates several integral inequalities held simultaneously for q and h-integrals in implicit form. These inequalities are established for symmetric functions using certain types of convex functions. Under certain conditions, Hadamard-type inequalities are deducible for q-integrals. All the results are applicable for ℏ-convex, m-convex and convex functions defined on the non-negative part of the real line. [ABSTRACT FROM AUTHOR]