臺灣博碩士論文加值系統

本篇論文主要目的是研究關於廣義極限 σ-limit 的 Korovkin type 近似定理的結果。我們除了給予σ-limit 及 aσ-limit 的一些基本結果。另外對於σ-limit 的 Korovkin type 近似定理，我們分成 pointwise, weakly convergence and norm convergence 三種情形討論。我們也引進 almost positive linear operators 的觀念。

This paper is concerned the results of Korovkin type approximation theorems related
with the generalized limits σ-limit and aσ-limit . We shall also study some basic properties
of σ-limit and aσ-limit . On the other hand, we study the Korovkin type approximation
theorems by departing into the following three situations: pointwise, weak convergence and
norm convergence. We shall introduce a new concept, so called almost positive linear operators.

1.Introduction………………………………………………………1

2.Some basic definition and results…………………………5

3.Pointwise approximation theorems of type σ-limit ………8

4.Approximation theorems of type σ-limit …………………16

5.Pointwise approximation theorems for almost positive
operator sequence…………………………………………………23

6.Approximation theorems for almost positive operator sequence……28

Reference……………………………………………………………31

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