... τ
3
> 0 = H
∞
(T v
1
, T v
2
).
(ii) For any m ≥ 3, we have
ϕ(d
∞
(v
1
, v
m
))d
∞
(v
1
, v
m
) + Ld
∞
(v
m
, T v
1
) = τ
3
+ Lτ
2
> τ
1
= H
∞
(T v
1
, T v
m
).
(iii) For any m ≥ 3, we obtain
ϕ(d
∞
(v
2
, ... x) for all x, y ∈ X with x = y. (3.7)
Then the following statements hold.
(a) there exists a Cauchy sequence {x
n
}
n∈N
in X such that
(i) x
n+1
∈ T x
n
for each n ∈ N;
(ii) i...