Table 3 Numerical results of Δ and θ for \(\psi _{3}(z)=\ln (z)\) and \(\eta \in \mathrm{J} = [1,e]\) in Example 5.1
η | \(\psi _{3}(z)= \ln (z)\), \(\rho =\frac{2}{3}\), \(\sigma =\frac{1}{3}\) | ||
|---|---|---|---|
Λ | Δ | \(\theta =0.2\geq \Delta [(\theta +1)^{\ell }-1 +N]\) | |
1.00 | 2.0000 | 0.0832 | 0.2>0.0893 |
1.10 | 1.8295 | 0.0882 | 0.2>0.0945 |
1.20 | 1.7883 | 0.0897 | 0.2>0.0961 |
1.30 | 1.7610 | 0.0908 | 0.2>0.0973 |
1.40 | 1.7404 | 0.0917 | 0.2>0.0983 |
1.50 | 1.7237 | 0.0924 | 0.2>0.0991 |
1.60 | 1.7098 | 0.0931 | 0.2>0.0998 |
1.70 | 1.6978 | 0.1053 | 0.2>0.1153 |
1.80 | 1.6873 | 0.1059 | 0.2>0.1160 |
1.90 | 1.6780 | 0.1065 | 0.2>0.1166 |
2.00 | 1.6696 | 0.1070 | 0.2>0.1172 |
2.10 | 1.6621 | 0.1075 | 0.2>0.1177 |
2.20 | 1.6552 | 0.1079 | 0.2>0.1182 |
2.30 | 1.6488 | 0.1083 | 0.2>0.1187 |
2.40 | 1.6429 | 0.1087 | 0.2>0.1191 |
2.50 | 1.6374 | 0.1091 | 0.2>0.1195 |
2.60 | 1.6323 | 0.1095 | 0.2>0.1199 |
2.70 | 1.6276 | 0.1098 | 0.2>0.1203 |