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Approximation properties of exponential type operators connected to p(x)=2x3/2

  • *Corresponding author: Voichiţa Adriana Radu

    *Corresponding author: Voichiţa Adriana Radu

Dedicated to Prof. Vijay Gupta on the occasion of his 60th birthday

Abstract / Introduction Full Text(HTML) Figure(3) / Table(1) Related Papers Cited by
  • In this paper, we provide a state-of-the-art survey of some recent results regarding approximation properties of exponential type operators connected with 2x3/2 obtained by professor Gupta and his collaborators in the last few years. The pioneer work in introduction and study of exponential type operators was due to May and Ismail, earlier, in 1976 and 1978. Gupta, generalized and deepened this study through his many works in recent years. We bring together in discussion and give all existence theorems for this specific operators and their modification and present all their approximation properties that was studied until now. In the final section, the theoretical results are analyzed by numerical examples.

    Mathematics Subject Classification: Primary: 41A25; Secondary: 41A30.

    Citation:

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  • Figure 1.  Rate of Convergence of Sλ(f;x)

    Figure 2.  Rate of Convergence of ˜Sλ(f;x)

    Figure 3.  Comparison for the estimation error of Sλ(x) and ˜Sλ(x)

    Table 7.1.  Comparison for the estimation error |f(x)Sλ(x)| and |f(x)˜Sλ(x)| for the function f(x)=x3e2x,x[0,7],λ=100

    x |f(x)S100(x)| |f(x)˜S100(x)|
    0.5 0.00465844948 0.00796944716
    1 0.0139420318 0.0164838375
    1.5 0.0214114531 0.0166652807
    2 0.0240303881 0.0125649409
    2.5 0.0221245628 0.0080660240
    3 0.01774079259 0.00467694649
    3.5 0.01285128572 0.00252789012
    4 0.00861564405 0.00129783776
    4.5 0.00543587270 0.00064065220
    5 0.003266789389 0.000306594987
    5.5 0.001886769274 0.000143092704
    6 0.001054404924 0.000065414944
    6.5 0.0005731575186 0.0000293889419
    7 0.0003043180925 0.0000130094449
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  • [1] U. Abel and V. Gupta, Rate of convergence of exponential type operators related to p(x)=2x3/2 for functions of bounded variation, Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Serie A. Matemáticas (RACSAM), 114 (2020), Paper No. 188, 8 pp. doi: 10.1007/s13398-020-00919-y.
    [2] U. AbelV. Gupta and V. Kushnirevych, Asymptotic expansions for certain exponential-type operators connected with 2x3/2, Mathematical Sciences, 15 (2021), 311-315.  doi: 10.1007/s40096-021-00382-9.
    [3] U. Abel, V. Gupta and M. Sisodia, Some new semi-exponential operators, Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Serie A. Matemáticas (RACSAM), 116 (2022), Paper No. 87, 12 pp. doi: 10.1007/s13398-022-01228-2.
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