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Student Number 86221007
Author Hua Ya-Hui(花雅惠)
Author's Email Address No Public.
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Department Mathematics
Year 1998
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title Pointwise approximation of functions of locally bounded variation via some integral operators
Date of Defense
Page Count 35
Keyword
  • Beta operator
  • Bleimann-Butzer-Hahn operator
  • Fourier-Legendre series
  • Hermite-Fejer operator
  • integral operator
  • locally bounded variation
  • Picard operator
  • pointwise approximation
  • Abstract
    Table of Content Chapter 1. Introduction and Preliminaries....................................... 1
    Chapter 2. Estimates for Approximation of Functions in BV ........ 5
    Chapter 3. Estimates for Approximation of Functions in DBV ....12
    Chapter 4. Estimates for Approximation of Functions in B_N and DB_N ...... 18
    Chapter 5. Applications ........................................ 25
    §1. Picard Operators .......................................... 25
    §2. Beta Operators ............................................. 27
    §3. Hermite-Fejer Operators .............................. 30
    §4. Fourier-Legendre Series ............................... 31
    §5. Bleimann-Butzer-Hahn Operators ............... 33
    References ............................................................. 34
    Reference [1] S. N. Bernstein, Demonstration du theoreme de Weierstrass, fondee sur le calcul des probabilites, Commun. Soc. Math. Kharkow (2) 13 (1912--13), 1--2.[2] G. Bleimann, P. L. Butzer and L. Hahn, A Bernstein-type operator approximatingcontinuous functions on the semi-axis, Indag. Math. 42 (1980), 255--262.[3] H. Bohman, On approximation of continuous and analytic functions, Ark. Math.2 (1952--54), 43--56.[4] R. Bojanic, An estimate for the rate of convergence of a general class of orthogonalpolynomial expansions of functions of bounded variation, Math. Anal. and itsApplications (Kuwait) (1985), 1--16.[5] R. Bojanic and F. Cheng, Estimates for the rate of approximation of functions ofbounded variation by Hermite-Fejer polynomials, Canadian Math. Soc. ConferenceProceeding 3 (1983), 5--17.[6] R. Bojanic and F. Cheng, Rate of convergence of Hermite-Fejer polynomials forfunctions with derivatives of bounded variation, Acta Math. Hung. 59 (1--2) (1992), 91--102.[7] R. Bojanic and M. K. Khan, Rate of convergence of some operators of functionswith derivatives of bounded variation, Atti. Sem. Mat. Fis. Univ. Modena, XXXIX(1991),495--512.[8] R. Bojanic and M. Vuilleumier, On the rate of convergence of Fourier-Legendreseries of functions of bounded variation, J. Approx. Theory 31 (1981), 67--79.[9] Y. S. Chow and H. Teicher, "Theory : Independence, Interchangeability,Martingales,"2nd ed., Springer-Verlag, New York, 1988.[10] R. A. DeVore, "Approximation of Continuous Functions by Positive LinearOperators,"Springer-Verlag, Berlin, 1972.[11] M. K. Khan, Approximation properties of beta operators, in "in ApproximationTheory"(P. Nevai and A. Pinkus, Eds.), pp. 483--495, Academic Press, Boston, 1991.[12] R. A. Khan, A note on a Bernstein-type operator of Bleimann, Butzer, and Hahn,J. Approx. Theory 53 (1988), 295--303.[13] P. P. Korovkin, On convergence of linear positive operators in the spaceof continuous functions, Dokl. Akad. Nauk SSSR 90 (1953), 961--964. [In Russian].[14] P. P. Korovkin, "Linear Operators and Approximation Theory,"Hindustan,Delhi, 1960.[15] H. R. Pitt, "and integration for use,"Oxford Univ. Press, 1987.[16] S.-Y. Shaw, W.-C. Liaw, and Y.-L. Lin, Rates for approximation offunctions in BV[a,b] and DBV[a,b] by positive linear operators, Chinese J. Math.21 (2)(1993), 171--193.[17] K. Weierstrass, Uber die analytische Darstellbarkeit sogenannter willkurlicherFunktionen einer reellen Veranderlichen, Sitzungsber. Akad. Berlin, 1885, 633--639,789--805.[18] 白國燈, 正線性算子對具有局部囿變差之指數有界函數的點態逼近行為,中央大學數學研究所碩士論文, 民國87年.
    Advisor
  • Shaw Sen-Yen(蕭勝彥)
  • Files No Any Full Text File.
    Date of Submission

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