I-Convergence of Korovkin Type Approximation Theorems for Unbounded Functions

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姓名

蔡志陽(Chih-Yang Tsai) 查詢紙本館藏

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數學系

論文名稱

(I-Convergence of Korovkin Type Approximation Theorems for Unbounded Functions)

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摘要(中)

本篇論文將先介紹較統計收斂與A-統計收斂更為一般化的理想收斂，研究主軸為正線性算子，並以理想收斂來討論無界連續函數空間上的Korovkin近似定理。更進一步將所討論的空間擴展至高維度算子值或實數值函數空間。

摘要(英)

The purpose of this thesis is to study a Korovkin type approximation of unbounded functions by means of ideal convergence. The concept of ideal convergence is the generalizations of statistical convergence and A-statistical convergence. We will discuss the approximations of unbounded, operator-valued and real-valued functions with noncompact supports in R^m.

關鍵字(中)

★ 理想收斂
★ Korovkin 近似型定理

關鍵字(英)

★ Korovkin type approximation theorem
★ I-convergence

論文目次

1.Introduction............................................1
2.Some basic definitions and results......................3
3.I-convergence of unbounded functions....................9
4.I-convergence of unbounded m-parameter functions.......16
5.Examples...............................................24
References...............................................35

參考文獻

[1] K. Demirci, I-limit superior and limit inferior, Math. Commun., 6 (2001), 165-172.
[2] O. Duman, M.K. Khan, and C. Orhan, A-statistical convergence of approximating operators, Math. Inequalities and Appl., 6 (2003), 689-699.
[3] O. Duman and C. Orhan, Statistical approximation by positive linear operators, Studia Math., 161 (2004), 187-197.
[4] O. Duman and C. Orhan, Rates of A-statistical convergence of positive linear operators, Applied Math. Letters, 18 (2005), 1339-1344.
[5] E. Erkus and O. Duman, A Korovkin type approximaiton theorem in statistical sense, Studia Sci. Math. Hungar., 43 (2006), 285-294.
[6] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
[7] A.R. Freedman and J.J. Sember, Densities and summability, Pacific J. Math., 95 (1981), 293-305.
[8] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32 (2002), 129-138.
[9] P.P. Korovkin, Linear Operators and Theory of Approximation, Hindustan Publ. Comp., Delhi, 1960.
[10] P. Kostyrko, M. Macaj, and T. Salat, I-convergence, Real Anal. Exchange, 26 (2000), 669-686.
[11] J.E. Marsden and M.J. Hoffman, Elementary Classical Analysis, 2nd ed., W.H. Freeman and Comp., 1993.
[12] H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Tran. Amer. Math. Soc., 347 (1995), 1811-1819.
[13] H.I. Miller and C. Orhan, Statistical (T) rates of convergence, Glasnik Matematicki, 39 (2004), 101-110.
[14] A. Nabiev, S. Pehlivan, and M. Gurdal, On I-Cauchy sequences, Taiwanese J. Math., 11 (2007), 569-576.
[15] S.-Y. Shaw, Approximation of unbounded functions and applications to representations of semigroups, J. Approx. Theory, 28 (1980), 238-259.
[16] S.-Y. Shaw and C.-C. Yeh, Rates for approximation of unbounded functions by positive linear operators, J. Approx. Theory, 57 (1989), 278-292.
[17] H. Steinhaus, Sur la convergence ordinarie et la convergence asymptotique, Colloq. Math., 2 (1951), 73-74.

指導教授

蕭勝彥、高華隆
(Sen-Yen Shaw、Hwa-Long Gau)

審核日期

2009-6-11

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