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In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities.

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In this paper, we use the modified homotopy perturbation method to solving the system of linear equations. We show that this technique enables us to find the exact solution of the system of linear equations. This technique is independent of the auxiliary parameter and auxiliary operator. Our results can be viewed as a novel improvement and an extension of the previously known results.

In this paper, we introduce a new class of convex functions which is called h ϕ -preinvex functions. We prove several Hermite-Hadamard inequalities for h ϕ -preinvex functions. Some special cases are also discussed. Results proved in this paper continue to hold for these special cases. Our results may stimulate further investigation regarding variant forms of Hermite-Hadamard type inequalities. Mathematics Subject Classification 26D15 · 26A51