S-iteration process for quasi-contractive mappings

Journal of Inequalities and Applications

Table 4 Oscillatory functions

Number of iterations	Noor iteration		Picard iteration		Mann iteration		Ishikawa iteration		Agarwal *et al.* iteration		S-iteration
n	${f x}_{n}$	$x_{n + 1}$	${f x}_{n}$	$x_{n + 1}$	${f x}_{n}$	$x_{n + 1}$	${f x}_{n}$	$x_{n + 1}$	${f x}_{n}$	$x_{n + 1}$	${f x}_{n}$	$x_{n + 1}$
0	1.25	1.25	1.25	1.25	1.25	1.25	1.25	0.8	1.25	0.8	1.25	0.8
1	0.8	0.921512	0.8	0.8	0.8	0.871597	1.25	0.840872	1.25	0.912469	1.25	0.848606
2	1.085173	1.022975	1.25	1.25	1.14732	1.081101	1.189241	0.889224	1.095928	0.985571	1.178403	0.909754
3	0.977541	0.997476	0.8	0.8	0.924983	0.970709	1.124576	0.930283	1.01464	0.999983	1.099198	0.95812
4	1.002531	1.000107	1.25	1.25	1.030175	1.010476	1.074942	0.95931	1.000017	1.000002	1.043711	0.984874
5	0.999893	1.000002	0.8	0.8	0.989632	0.997158	1.042416	0.977477	0.999998	1	1.015358	0.995667
6	0.999998	1	1.25	1.25	1.00285	1.000657	1.023042	0.987967	1	1	1.004352	0.998995
7	1	1	0.8	0.8	0.999343	0.999876	1.01218	0.99372	1	1	1.001006	0.999809
8	1	1	0.8	0.8	1.000124	1.000019	1.00632	0.996772	1	1	1.000191	0.99997
9	1	1	1.25	1.25	0.999981	0.999998	1.003238	0.998358	1	1	1.00003	0.999996
10	1	1	0.8	0.8	1.000002	1	1.001645	0.99917	1	1	1.000004	1
11	1	1	0.8	0.8	1	1	1.000831	0.999583	1	1	1	1
12	1	1	1.25	1.25	1	1	1.000418	0.999791	1	1	1	1
13	1	1	0.8	0.8	1	1	1.000209	0.999895	1	1	1	1
14	1	1	0.8	0.8	1	1	1.000105	0.999948	1	1	1	1
15	1	1	1.25	1.25	1	1	1.000052	0.999974	1	1	1	1
16	1	1	0.8	0.8	1	1	1.000026	0.999987	1	1	1	1
17	1	1	1.25	1.25	1	1	1.000013	0.999993	1	1	1	1
18	1	1	0.8	0.8	1	1	1.000007	0.999997	1	1	1	1
19	1	1	1.25	1.25	1	1	1.000003	0.999998	1	1	1	1
20	1	1	0.8	0.8	1	1	1.000002	0.999999	1	1	1	1
21	1	1	1.25	1.25	1	1	1.000001	1	1	1	1	1
22	1	1	0.8	0.8	1	1	1	1	1	1