On continuing this, we generate a sequence ({hx_{n}}_{n=1}^{infty}) as follows: (Sx_{n}=hx_{n+1}) for each n.
By continuing this, we generate a sequence ({hx_{n}}_{n=1}^{infty}) as follows: (Sx_{n}=hx_{n+1}) for each n.
Continuing this process, we construct sequences {x n }, {y n }, and {z n } in X such that g x n + 1 = F ( x n, y n, z n ), g y n + 1 = F ( y n, x n, z n ), and g z n + 1 = F ( z n, y n, x n ).
Continuing this process yields an infinite sequence of nested intervals, labeled by an infinite sequence of digits b0, b1, b2, b3,..., and one writes :x = b_0.b_1b_2b_3 \dots.
Continuing this procedure we get a sequence satisfying (3.2).
Continuing this process, we get a sequence in, such that and (2.10).
Continuing this process, we obtain a sequence ({y_{n}}) in B such that (d y_{n+1},Ty_{n})=d(A,B)).
Continuing this process successively yields a sequence of solutions satisfying (3.12).
Continuing this process, we construct a sequence (x n ) in X such that x2n= Tx2n+1all x2n+1= Sx2n+2for all n ∈ N ∪ {0}.
Continuing this process, we obtain a sequence ({x_{n}}) in A, such that (d(x_{n+1},Tx_{n})=d(A,B)).
