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In this paper, a new integral identity is provided. Based on this equality, Simpson-type dual integral inequalities for functions whose first derivatives are s-convex via Riemann–Liouville fractional integrals are established. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a new parameterized identity that generates a quadrature rule family similar to Simpson's second formula, and then we establish some new Simpson-like type inequalities for functions whose first derivatives are s-convex in the second sense, from which we can deduce the famous 3 8 -Simpson inequality. We end the article with some applications. [ABSTRACT FROM AUTHOR]

In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we give some Minkowski–Clarkson's type inequalities related to two finite sequences of real nonnegative numbers. In particular, we prove two inequalities which in some sense can be regarded as inverse Minkowski's inequalities concerning the cases p ≥ 2 {p\geq 2} and 0 < p ≤ 1 {0

In this paper, we will prove some new dynamic inequalities on time scales. These inequalities as special cases contain some integral and discrete inequalities due to Hardy and Copson. The main results will be proved by using the Hölder inequality and a simple consequence of Keller's chain rule on time scales. [ABSTRACT FROM AUTHOR]

In this paper we introduce new refinements of both the discrete and the classical Jensen's inequality. First, we give the weighted version of a recent cyclic refinement. By using this result, we obtain new refinements of the classical Jensen's inequality. We investigate m-exponential convexity of some functionals coming from the new refinements. To apply our results we define some new mixed symmetric means, generalized means, and Cauchy means, and study their properties. [ABSTRACT FROM AUTHOR]

In this paper, some refinements of Hermite-Hadamard type inequalities for GA-convex functions are obtained. Applications of the obtained results to special means are given. [ABSTRACT FROM AUTHOR]

Natural phenomena as well as problems encountered in pure and applied sciences are modeled by ordinary, partial or integral differential equations. Most of these problems have a nonlinear aspect which makes their studies difficult, or even impossible. For this, they must resort to other alternatives; among the methods used is the integral inequalities approach, which allows the study of quantitative and qualitative properties of solutions such as existence, uniqueness, delimitation, oscillation, and stability. In this study, we present some new integral inequalities of the Gronwall–Bellman–Bihari type associated with the fractional derivative of ψ-Hilfer, which represents a strong tool and is applicable in the study of certain differential equations. Several known results are derived and some applications to ordinary differential equations are provided to demonstrate the effectiveness of our finding. [ABSTRACT FROM AUTHOR]

We consider the sequential CFC-type nabla fractional difference (CFC ∇ a + 1 ν ∇ a μ CFC u) (t) {(^{\mathrm{CFC}}\nabla^{\nu}_{a+1}{}^{\mathrm{CFC}}\nabla^{\mu}_{a}u)(t)} and show that one can derive monotonicity-type results even in the case where this difference satisfies a strictly negative lower bound. This illustrates some dissimilarities between the integer-order and fractional-order cases. [ABSTRACT FROM AUTHOR]

We present some initial results for detecting extrema of a function when the only a priori information is some limited pointwise data about f as well as information about an appropriate fractional difference of f. In particular, such results provide some analogues of the well-known tests for detecting local extrema using the sign of . Certain of these results are consequences of some new monotonicity conditions, which relate conditions on the sign of , for , to the monotonicity of f. Finally, we provide some numerical examples to illustrate the results. [ABSTRACT FROM AUTHOR]

Some double integral inequalities of Hermite-Hadamard type for h-convex functions defined on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. [ABSTRACT FROM AUTHOR]