Table 3 The comparison results of upper bounds \(h_{2}\) with different \(h_{1}\) for \(\mu = 0.5\) (Example 2)

E. Fridman et al. [9] Theorem 1

1.5652

2.3987

3.1450

4.2225

5.1607

6.0109

7.2547

H.Y. Shao [6] Theorem 1

1.7586

2.5006

3.2061

4.3531

5.2209

6.1313

7.3135

J. Sun et al. [10] Theorem 2

1.9186

2.6112

3.3472

4.4845

5.3925

2.2204

7.4996

P.G. Park et al. [26] Theorem 2

2.1011

2.7831

3.4879

4.5249

5.4029

6.3007

7.5505

A. Seuret et al. [31] Theorem 1

2.2960

2.8016

3.5111

4.6919

5.6212

6.5492

7.7713

Theorem 2

2.4811

2.9931

3.6080

4.8150

5.7930

6.7219

7.9716