Abstract In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using established identity, offer some Simpson’s type inequalities co-ordinated convex functions in a rectangle from plane $\mathbb{R} ^{2}$ R 2 </mml:msu...

In this paper, we establish a link between maximizing (information-theoretic) entropy and the construction of polygonal interpolants. The determination of shape functions on n-gons (n > 3) leads to a non-unique under-determined system of linear equations. The barycentric co-ordinates i , which form a partition of unity, are associated with discrete probability measures, and the linear reproduci...

Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the dual systems. We demonstrate that the Θ-function coefficients of their expansion can be expressed entirely in terms of the co-ordinates of the Seiberg-Witten integrable system, being, th...

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

We discuss in this paper a method of finding skyline or non-dominated points in a set P of nP points with respect to a set S of nS sites. A point pi ∈ P is non-dominated if and only if for each pj ∈ P , j 6= i, there exists at least one point s ∈ S that is closer to pi than pj . We reduce this problem of determining non-dominated points to the problem of finding sites that have non-empty cells ...

1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are smooth (i.e. of class C). In terms of local co-ordinates (x, x, ...,x") on M and local co-ordinates (y,y, •••,/") on M', the riemannian metrics are written ds = gtJ dx l dx, ds' = g'aP dy* dy * wher...