Two Continuity Concepts In Approximation Theory

Approximation theory - moduli of continuity and global smoothness preservation

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Some New Continuity Concepts for Metric Projections

Approximation of Indistinct Concepts

This theory on semi-equivalence relations is an important and useful tool for investigating classification, pattern recognition, polling and inference etc. Based on it, this paper presents a new framework, in which an indistinct concept, that is one with incomplete or undetermined information about the objects, can be represented approximately. Such an approximate representation will reflect de...

Continuity Properties of Best Analytic Approximation

Let A be the operator which assigns to each m×n matrix-valued function on the unit circle with entries in H∞+C its unique superoptimal approximant in the space of bounded analytic m × n matrix-valued functions in the open unit disc. We study the continuity of A with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, A is continuous at any f...

Relations between Various Continuity Concepts in Effect Algebras

The aim of the present paper is to establish relations between continuity concepts for a nonnegative extended real-valued function μ defined on an effect algebra. Examples and counterexamples are given to illustrate various situations arising in this study.