Fixed points of a new type of contractive mappings in complete metric spaces

Table 1 The comparison of Banach contraction condition with F-contraction condition

n	x_n	$C_{F_{1}} (S_{1}, S_{n})$	$C_{F_{2}} (S_{1}, S_{n})$
3	378	0.91629	3.91629
4	351	0.58779	4.58779
5	325	0.44183	5.44183
6	300	0.35667	6.35667
7	276	0.30010	7.30010
8	253	0.25951	8.25951
9	231	0.22884	9.22884
10	210	0.20479	10.20479
11	190	0.18540	11.18540
12	171	0.16942	12.16942
13	153	0.15600	13.15600
14	136	0.14458	14.14458
15	120	0.13473	15.13473
16	105	0.12615	16.12615
17	91	0.11861	17.11861
18	78	0.11192	18.11192
19	66	0.10595	19.10595
20	55	0.10059	20.10059
21	45	0.09575	21.09575
22	36	0.09135	22.09135
23	28	0.08734	23.08734
24	21	0.08367	24.08367
25	15	0.08030	25.08030
26	10	0.07719	26.07719
27	6	0.07431	27.07431
28	3	0.07164	28.07164
29	1	0.06916	29.06916
30	1	0.06684	30.06684
⋮	⋮	⋮	⋮
3 ×10⁴	1	6.66667 ×10^-5	30000.00007
n → ∞	T 1 = 1	tends to 0	≥ τ = 1

The generated iterations start from a point x₀ = S₂₉ = 435. C_F(S₁, S_n) denotes F(d(S₁, S_n)) - F(d(T(S₁), T(S_n)))