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This paper investigates several integral inequalities held simultaneously for <i>q</i> and <i>h</i>-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 <i>q</i>-integrals. All the results are applicable for <i>ℏ</i>-convex, <i>m</i>-convex and convex functions defined on the non-negative part of the real line.