Mean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative...

The methods of defining and evaluating evolution of information in economic systems are often based on abstract measuretheoretic mean-preserving transformations (MPTs), also known as second-order stochastic dominance. This study first points out that such abstract MPTs have distributional equivalents and then shows that the distributional MPTs often provide analytical settings that are more acc...

We develop a parallel theory to that concerning the concept of integral mean value of a function, by replacing the additive framework with a multiplicative one. Particularly, we prove results which are multiplicative analogues of the Jensen and Hermite-Hadamard inequalities. 1. Introduction Many results in Real Analysis exploits the property of convexity of the subintervals I of R; (A) x; y 2 I...

s for MAIA 2007 The limits of bivariate Lagrange projectors Carl de Boor∗ and Boris Shekhtman Eastsound, Washington In a talk in Norway in 2003, the first author conjectured that any finite-rank ideal projector (i.e., finite-rank linear projector on the space of polynomials in d variables whose kernel is a polynomial ideal, i.e., a linear space also closed under pointwise multiplication by poly...

In this note we give a subdifferential mean value inequality for every continuous Gâteaux subdifferentiable function f in a Banach space which only requires a bound for one but not necessarily all of the subgradients of f at every point of its domain. We also give a subdifferential approximate Rolle’s theorem stating that if a subdifferentiable function oscillates between −ε and ε on the bounda...

Mean value analysis is an exact solution technique for infinite capacity queueing networks and enjoyed widespread popularity during recent years. It considers the behavior of the system by stepwise increasing the number of jobs in the entire network, thus it is well-suited for the analysis of queueing networks with blocking. In this work, an approximation is introduced for the mean value analys...

We consider an extremal problem for polynomials, which is dual to the well-known Smale mean value problem. We give a rough estimate depending only on the degree.

‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

we describe a variational problem on a surface under a constraintof geometrical character. necessary and sufficient conditions for the existence ofbifurcation points are provided. in local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. the problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

Volume 16, No. 1 TRANSACTIONS 1