Table 1 Numerical results of Δ and θ for \(\psi _{1}(z)=z\) and \(\eta \in \mathrm{J} = [0,1]\) in Example 5.1
η | \(\psi _{1}(z)= z\), \(\rho =\frac{1}{4}\), \(\sigma =\frac{1}{2}\) | ||
|---|---|---|---|
Λ | Δ | \(\theta =0.2\geq \Delta [(\theta +1)^{\ell }-1 +N]\) | |
0.00 | 2.0000 | 0.0831 | 0.2>0.0891 |
0.05 | 1.9159 | 0.0856 | 0.2>0.0918 |
0.10 | 1.8811 | 0.0868 | 0.2>0.0931 |
0.15 | 1.8543 | 0.0877 | 0.2>0.0941 |
0.20 | 1.8318 | 0.0886 | 0.2>0.0950 |
0.25 | 1.8119 | 0.0893 | 0.2>0.0958 |
0.30 | 1.7940 | 0.0901 | 0.2>0.0966 |
0.35 | 1.7775 | 0.0908 | 0.2>0.0973 |
0.40 | 1.7621 | 0.0914 | 0.2>0.0980 |
0.45 | 1.7477 | 0.0920 | 0.2>0.0987 |
0.50 | 1.7340 | 0.0926 | 0.2>0.0993 |
0.55 | 1.7211 | 0.0932 | 0.2>0.1000 |
0.60 | 1.7087 | 0.1056 | 0.2>0.1156 |
0.65 | 1.6968 | 0.1062 | 0.2>0.1163 |
0.70 | 1.6853 | 0.1068 | 0.2>0.1170 |
0.75 | 1.6743 | 0.1074 | 0.2>0.1176 |
0.80 | 1.6636 | 0.1079 | 0.2>0.1182 |
0.85 | 1.6532 | 0.1085 | 0.2>0.1189 |
0.90 | 1.6432 | 0.1091 | 0.2>0.1195 |
0.95 | 1.6334 | 0.1096 | 0.2>0.1201 |
1.00 | 1.6239 | 0.1102 | 0.2>0.1207 |