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This paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals. We also prove some new midpoint-type inequalities for q-differentiable convex functions. Moreover, we present some examples to illustrate our established results, supplemented with graphs. [ABSTRACT FROM AUTHOR]

In this article, we establish two new and different versions of fractional HermiteHadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson’s type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson’s type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Hölder’s inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results. [ABSTRACT FROM AUTHOR]

In this work, Hermite-Hadamard type inequalities for subadditive functions via quantum integrals are established. Moreover, Hermite-Hadamard type inequalities for the product of two subadditive functions are also obtained. It is worth to mentioning that some existing inequalities of Hermite-Hadamard type for subadditive functions are obtained by considering the limit of the real number q ∈ (0,1) as q → 1− in the key results. [ABSTRACT FROM AUTHOR]

In this paper, we establish Hermite-Hadamard inequalities for subadditive functions, and we give some related inequalities according to Hermite-Hadamard inequalities, which generalized the previously published results. [ABSTRACT FROM AUTHOR]