This paper deals with a delayed three-level food chain model with Beddington-DeAngelis functional response. By using the differential inequality theory, a set of sufficient conditions are obtained for the permanence of the system. By constructing a suitable Liapunov function, we derive that the system has a unique asymptotically periodic solution which is globally asymptotically stable. An exam...

The U.K. skill premium fell from the 1950s to the late 1970s and then rose very sharply. This paper examines the contributions to these relative wage movements of international trade and technical change. We first measure trade as changes in product prices and technical change as TFP growth. Then we relate price and TFP changes to a set of underlying factors. Among a number of results, we find ...

A variant of Jessen’s inequality for superquadratic functions is proved. This is a refinement of a variant of Jessen’s inequality of Mercer’s type for convex functions. The result is used to refine some comparison inequalities of Mercer’s type between functional power means and between functional quasi-arithmetic means.

We deal with a conditional functional inequality x ⊥ y ⇒ ‖ f (x + y)− f (x)− f (y) ‖ ≤ (‖ x‖ + ‖ y‖ ), where ⊥ is a given orthogonality relation, is a given nonnegative number, and p is a given real number. Under suitable assumptions, we prove that any solution f of the above inequality has to be uniformly close to an orthogonally additive mapping g, that is, satisfying the condition x ⊥ y ⇒ g(...

The robust stability analysis of asynchronous and uncertain sampled-data systems with constant incremental input delay is addressed in the looped-functional framework. These functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete-time stability conditions in an affine way, enabling then the consideration of uncertain and time-varyin...

Keywords: Diamond-α integral Time scale Hölder inequality Minkowski's inequality a b s t r a c t In this paper, we establish a functional generalization of the diamond-α integral reverse Hölder inequality on time scales. Some related inequalities are also considered.

In the article, a functional inequality in abstract spaces is established, which gives a new affirmative answer to an open problem posed by Feng Qi in [9]. Moreover, some integral inequalities and a discrete inequality involving sums are deduced.

A four part dissection and rearrangement provides a new proof of the isoperimetric inequality in the plane as well as a new approach to Bonnesen-type error estimates for the isoperimetric deficit of compact convex sets and of star bodies that are centrally symmetric with respect to the origin. An isoperimetric inequality in R bounds the area (or related functional) of a compact set by some func...

Abstract In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension Jensen’s functional for n -convex functions is deduced from inequality involving diamond integrals. Special conditions, including Taylor two point formula Lagrange’s interpolation, are also deployed to find further extensions functional. This paper includes discussion on bounds Grüss ine...

Inspired by the forward and the reverse channels from the image-size characterization 1 problem in network information theory, we introduce a functional inequality which unifies 2 both the Brascamp-Lieb inequality and Barthe’s inequality, which is a reverse form of the 3 Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using 4 the Legendre-Fenchel dualit...