Further Extensions of a Legendre Function Integral

Further Extensions of a Legendre Function Integral

Legendre-type integrands and convex integral functions

In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

A Legendre-spectral scheme for solution of nonlinear system of Volterra-Fredholm integral equations

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

Extensions of Several Integral Inequalities

In this article, an open problem posed in [12] is studied once again, and, following closely theorems and methods from [5], some extensions of several integral inequalities are obtained.

INTEGRAL EXTENSIONS AND THE a-INVARIANT

In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if A ⊂ B is a finite homogeneous inclusion of standard graded domains over an algebraically closed field with A normal and B of minimal multiplicity then A has minimal multiplicity. In some sense these results are algebraic generalizations of Hurwitz type theorems.