Successive Approximation of Implicit Multistep Type Iterative Algorithms in Locally Convex Spaces

Riesz Type Theorem in Locally Convex Spaces

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely Theorem. If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T : C[a, b] → X is of the form Tg = ∫ b a g(t)dx(t), where the function x(·) : [a, b] → X has a weakly compact semivariation on [a, b]. This th...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Asymmetric locally convex spaces

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

A Successive Minima Method for Implicit Approximation

This paper is concerned with the problem of approximating a collection of unorganized data points by an algebraic tensor-product B-spline curve. The implicit approximation to data points would be ideally based on minimizing the sum of squares of geometric distance. Since the geometric distance from a point to an implicit curve cannot be computed analytically, Sampson distance, which is the firs...