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In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking q → 1 −. Finally, we give mathematical examples of convex functions to verify the newly established inequalities. [ABSTRACT FROM AUTHOR]

T.Z. Mirkovic [14] obtained new inequalities of Wirtinger type by using some classical inequalities and special means for convex function. So in this paper, we obtain some inequalities of Wirtinger type for s-convex function, m-convex function, (α,m)-convex function, quasi-convex function and P-function. Also several special cases are discussed, which can be deduced from our main results. [ABSTRACT FROM AUTHOR]

In this paper, the authors established a new identity for differentiable functions, afterwards they obtained some new inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. Also they give some applications for special means for arbitrary positive numbers. [ABSTRACT FROM AUTHOR]

In this paper, some new integral inequalities of Hermite-Hadamard type are presented for functions whose nth derivatives in absolute value are s-logarithmically convex. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are s-logarithmically convex functions as special cases. Our results may provide refinements of some results for s-logarithmically convex functions already exist in literature. Finally, applications to special means of the established results are given. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new integral inequalities for convex and m–convex functions by using a new kernel. The analysis used in the proofs is fairly elementary and based on the classical inequalities. We also give some comparisons and applications to special means for our results. [ABSTRACT FROM AUTHOR]

The authors have recently introduced a new generalized derivative operator μλ1,λ2n,m, that generalized many well-known operators. The trend of finding new differential or integral operators has attracted widespread interest. The aim of this paper is to use the relation ... to discuss some interesting results by using the technique of differential subordination. The results include both subordination and inclusion. In the case of n = 0,λ2 = 0, we obtain the results of Oros [11]. [ABSTRACT FROM AUTHOR]