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標題: 關於 σ-limit 的 Korovkin 型近似定理
Korovkin Type Approximation Theorem Related with σ-limit
作者: 張峻國
Chang, Chun-Kuo
關鍵字: Korovkin;近似定理;approximation theorem;σ-limit;aσ-limit;廣義極限;弱收歛;強收斂
出版社: 應用數學系所
引用: [1] Robert B. Ash, “Probability and Measure Theory”, 2nd ed., San Diego :Harcourt/ Academic Press,c2000. [2] Francesco Altomare & Michele Campiti, “Korovkin-type Approximation Theory and Its Applications”, Berlin ;W. de Gruyter, New York, 1994. [3] Juan Hernandez Guerra & Daniel Cardenas-Morales, Qualitative Korovkintype results on almost convergence, Monografias del Semin. Matem. Garcia de Galdeano. 27: 2003, 331-336. [4] Chifung Li, Some results about sσ-limit and a representation theorem of sequences in a reflexive Banach space, master dissertation of NCU in Taiwan, 2002. [5] Y.-C. Li, Almost convergence of sequences in a Banach spaces in weak, strong, and absolute senses, Taiwanese journal of mathematics Vol. 10(1) (2006), 209-218. [6] Y.-C. Li and S.-Y. Shaw, Generalized limits and a mean ergodic theorem, Studia Math. 121 1996, 207-219. [7] Sanny Li, Chifung Li, and Yuan-Chuan Li, On σ-limit and aσ-limit in Banach spaces. Taiwanese journal of mathematics Vol. 9(3) (2005) 359-371. [8] G. G. Lorentz, A contribution to the theory of divergent sequence, Acta Math. 80 1948, 167-190. [9] P. P. Korovkin, “Linear Operators and Approximation Theory”, Hindustan Publishing Corp., Delhi, India, 1960. [10] J.A. De Reyna, “Pointwise Convergence of Fourier Series”, New York: Berlin; Springer, c2002. [11] Walter Rudin, “Real and Complex Analysis”, 3rd ed., New York: McGraw-Hill, 1987. [12] Kˆosaku Yosida, ”Functional Analysis”, 6th ed., New York: Springer-Verlag Berlin Heidelberg, 1980. [13] Z. Ditzian, V. Totik, “Moduli of Smoothness“, New York: Berlin; Springer-Verlag, 1987.
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.
其他識別: U0005-3006200815101600
Appears in Collections:應用數學系所

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