Table 1 The convergence step of \(\lbrace x_{n} \rbrace \) for example with \(\alpha _{n} = 0.1 + \frac{0.000001}{n^{2}}\) and \(\beta _{n} = 0.005+\frac{0.0000001}{n^{2}}\)

0.0

3.92118419

3.92242687

1.30160882

3.92242687

0.1

3.36671997

3.37519562

1.65351070

3.37519562

0.2

2.82465927

2.83754278

2.35571598

2.83754278

0.3

2.40370170

2.41804592

2.40900977

2.41804592

0.4

2.07028621

2.08442445

2.14697656

2.08442445

0.5

1.80172064

1.81466881

1.87174319

1.81466881

0.6

1.58221589

1.59335578

1.63868670

1.59335578

0.7

1.40051118

1.40941688

1.44510892

1.40941688

0.8

1.24840048

1.25474044

1.28251199

1.25474044

0.9

1.11978947

1.12326988

1.14342745

1.12326988

1.0

1.01007550

1.01040682

1.02099028

1.01040682