Table 2 Error of approximation process for \(\tilde{g}(x)=-\frac{x}{2}+\frac{1}{10+x^{2}+x^{3}}+\sqrt{x}\)
From: Approximation with Szász-Chlodowsky operators employing general-Appell polynomials
\({{E}_{n}}\) n= | Error bound at | |||||
|---|---|---|---|---|---|---|
x = 0.2 | x = 0.4 | x = 0.6 | x = 0.8 | x = 1.0 | ||
\(b_{n}=n^{\frac{1}{4}}\) | 20 | 0.147529 | 0.12774 | 0.104113 | 0.0789145 | 0.0515653 |
50 | 0.110057 | 0.0990441 | 0.084131 | 0.0639238 | 0.0392311 | |
100 | 0.0937739 | 0.0909359 | 0.0787186 | 0.0594359 | 0.0351593 | |
\(b_{n}=n^{\frac{1}{6}}\) | 20 | 0.132132 | 0.114179 | 0.0941172 | 0.0714188 | 0.0455463 |
50 | 0.0985856 | 0.0931308 | 0.0802711 | 0.0607755 | 0.0363954 | |
100 | 0.0877984 | 0.0881726 | 0.0765825 | 0.0575355 | 0.0333826 | |
\(b_{n}=n^{\frac{1}{8}}\) | 20 | 0.125123 | 0.108813 | 0.0904582 | 0.0687138 | 0.0433252 |
50 | 0.0944476 | 0.0912384 | 0.0789394 | 0.0596288 | 0.0353382 | |
100 | 0.0860583 | 0.0872578 | 0.0758307 | 0.0568539 | 0.032739 | |