Vol. II. Chapter III. Generalizations of the Notion of a Basis.- 0. Banach spaces which do not have the approximation property.- I. Countable Generalizations of Bases.- 1. Basic sequences. Bibasic… Expand

Abstract Convexity of Elements of a Complete Lattice. Abstract Convexity of Subsets of a Set. Abstract Convexity of Functions on a Set. Abstract Quasi-Convexity of Functions on a Set. Dualities… Expand

We study topical and sub-topical functions (i.e., functions which are increasing in the natural partial ordering of ℝn and additively homogeneous, respectively additively sub-homogeneous), and… Expand

High-order finite difference methods for solving the Helmholtz equation are developed and analyzed, in one and two dimensions on uniform grids. The standard pointwise representation has a… Expand

We introduce and study the Abadie constraint qualification, the weak Pshenichnyi--Levin--Valadier property, and related constraint qualifications for semi-infinite systems of convex inequalities and linear inequalities.Expand

We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation… Expand

The aim of the present paper is to develop a theory of best approximation by elements of so-called normal sets and their complements-conormal sets-in the non-negative orthant R^I"+ of a… Expand

We develop a theory of downward subsets of the space ℝI, where I is a finite index set and T is an arbitrary index set, and we give some characterizations of best approximations by downward sets.Expand