Table 2 Comparison of Theorems 4.1 and 4.4 (Reich et al. [40]) with different values of \(\mu _{k}\)

Theorem 4.1 (μ = 0.15)

13

18

15

0.03426

0.04521

0.03218

Theorem 4.1 (μ = 0.35)

12

17

14

0.04036

0.08146

0.05919

Theorem 4.1 (μ = 0.75)

11

15

12

0.05731

0.09032

0.07984

Theorem 4.1 (μ = 0.95)

10

14

11

0.09104

1.09821

0.09978

Theorem 4.4 (Reich et al. [40])

57

67

49

2.93910

3.12310

2.11351