Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces

Table 1

Results of recurrence relations.

𝑛	𝜂𝑛	𝛽𝑛	𝑎𝑛	𝑏𝑛	𝑐𝑛
0	2.2882𝑒−001	1.9454	2.2257𝑒−001	5.0928𝑒−002	1.3343𝑒−002
1	3.0530𝑒−003	2.6520	4.0483𝑒−003	1.2360𝑒−005	4.7865𝑒−010
2	1.4613𝑒−012	2.6628	1.9456𝑒−012	2.8432𝑒−024	2.5141𝑒−047
3	3.6740𝑒−059	2.6628	4.8916𝑒−059	1.7972𝑒−117	1.0045𝑒−233
4	3.6904𝑒−292	2.6628	4.9134𝑒−292	0	0