Trigonometric approximation of functions in L1-norm

被引：0
|
作者：
Chandra, Prem [1 ]
Karanjgaokar, Varsha [2 ]
机构：
[1] Vikram Univ, C-315, Ujjain 456010, Madhya Pradesh, India
[2] Govt NPG Coll Sci, Dept Math, Raipur 492010, Madhya Pradesh, India
来源：
PERIODICA MATHEMATICA HUNGARICA | 2022年 / 84卷 / 02期
关键词：
Trigonometric Approximation of Functions; L-1 Approximation of functions; Degree of Approximation; Cesaro; Norlund methods;
D O I：
10.1007/s10998-021-00397-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the authors have obtained L-1-approximations of functions f in Lip(alpha, 1) (0 < alpha <= 1) by trigonometrical polynomials N-n(f; x) whenever the nonnegative and nonincreasing sequence (p(n)) satisfies certain conditions. This enables the authors to approximate f is an element of Lip(alpha, p) (0 < alpha <= 1, 1 <= p < infinity) in L-p-norm by trigonometrical polynomials sigma(beta)(n)(f; x) (beta > 0).
引用
收藏
页码：177 / 185
页数：9
相关论文
共 50 条
  • [1] TRIGONOMETRIC POLYNOMIAL-APPROXIMATION IN THE L1-NORM
    PEHERSTORFER, F
    [J]. MATHEMATISCHE ZEITSCHRIFT, 1979, 169 (03) : 261 - 269
  • [2] Concentration of the L1-norm of trigonometric polynomials and entire functions
    Malykhin, Yu. V.
    Ryutin, K. S.
    [J]. SBORNIK MATHEMATICS, 2014, 205 (11) : 1620 - 1649
  • [3] The L1-Norm of a Trigonometric Sum
    K. M. Éminyan
    [J]. Mathematical Notes, 2004, 76 : 124 - 132
  • [4] The L1-norm of a trigonometric sum
    Éminyan, KM
    [J]. MATHEMATICAL NOTES, 2004, 76 (1-2) : 124 - 132
  • [5] On trigonometric approximation of functions in the L-q norm
    Mohapatra, Ram N.
    Szal, Bogdan
    [J]. DEMONSTRATIO MATHEMATICA, 2018, 51 (01) : 17 - 26
  • [6] Approximation in L1-norm by elements of a uniform algebra
    Khavinson, D
    Perez-Gonzalez, F
    Shapiro, HS
    [J]. CONSTRUCTIVE APPROXIMATION, 1998, 14 (03) : 401 - 410
  • [7] REPRESENTATION OF EXTREMAL-FUNCTIONS IN THE L1-NORM
    PEHERSTORFER, F
    [J]. JOURNAL OF APPROXIMATION THEORY, 1979, 27 (01) : 61 - 75
  • [8] On the L1-norm Approximation of a Matrix by Another of Lower Rank
    Tsagkarakis, Nicholas
    Markopoulos, Panos P.
    Pados, Dimitris A.
    [J]. 2016 15TH IEEE INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND APPLICATIONS (ICMLA 2016), 2016, : 768 - 773
  • [9] Extensions of Moricz Classes and Convergence of Trigonometric Sine Series in L1-Norm
    Chouhan, Sandeep Kaur
    Kaur, Jatinderdeep
    Bhatia, Satvinder Singh
    [J]. MATHEMATICS, 2018, 6 (12)
  • [10] Low Rank Approximation with Entrywise l1-Norm Error
    Song, Zhao
    Woodruff, David P.
    Zhong, Peilin
    [J]. STOC'17: PROCEEDINGS OF THE 49TH ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING, 2017, : 688 - 701
12345