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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]

We have established this paper on m convex functions, which can be expressed as a general form of the convex function concept. First of all, some inequalities of Hadamard type are proved with fairly simple conditions. Next, an integral identity containing Atangana-Baleanu fractional integral operators is obtained to prove new inequalities for differentiable m-convex functions. Using this identity, various properties of m convex functions and classical inequalities, some new integral inequalities have been proved. [ABSTRACT FROM AUTHOR]

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 paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some Hermite-Hadamard type inequalities for uniformly convex functions with respect to geodesic in Hadamard space. Also, we give some application of these functions in means. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and M be an R-module. The aim of this paper is to introduce the notion of S-copure submodules and investigate some properties of this class of modules. We say that a submodule N of M is S-copure if there exists an s ∈ S such that s(N :M I) ⊆ N + (0 :M I) for every ideal I of R. [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, we establish new weighted integral inequalities for differentiable hconvex and quasi-convex functions. Applications of our findings to continuous random variables and approximation of integrals are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (p,ϕh)-convex functions and present some properties and representation of such functions. Finally, a version of Hermite Hadamard-type inequalities for (p,ϕh)-convex functions are established. [ABSTRACT FROM AUTHOR]

In this paper, some new weighted Simpson's type integral inequalities are presented for the class of harmonically-preinvex functions by using power-mean integral inequality and Holder's integral inequality. [ABSTRACT FROM AUTHOR]