Suppose that the pairs and satisfy the common property (E.A), then there exist two sequences and in such that (3.16).
Since the pairs and share the common property (E.A ., then there exist two sequences and in such that (3.6).
Proof If the pairs ( A, S ) and ( B, T ) satisfy the ( CLR S T ) property, then there exist two sequences { x n } and { y n } in X such that lim n → ∞ A x n = lim n → ∞ S x n = lim n → ∞ B y n = lim n → ∞ T y n = z, where z ∈ S ( X ) ∩ T ( X ).
(ii) Since Y is not normal, then there exist two sequences ( x n ) and ( y n ) in Y such that 0 ⪯ x n ⪯ y n for all n, y n → 0 and x n ↛ 0. Let us consider ( x n ) as a sequence in X.
Continuity: If x ∈ [ a, b ] and w ∈ I = ( lim inf z → x F φ ( z ), lim sup y → x F φ ( y ) ), Continuity: If x ∈ [ a, b ] and w ∈ I = ( lim inf z → x F φ ( z ), lim sup y → x F φ ( y ) ), then there exist two sequences y n, z n → x with F φ ( z n ) < w < F φ ( y n ).
And there exist two sequences and with,, such that and.
And there exist two sequences and with (4.1).
Since is dense in, there exist two sequences and in such that and as.
As both the pairs share the common property, there exist two sequences such that (3.21).
A function is said to be oscillatory on if there exist two sequences, such that and as moreover.
In view of Lemma 3.1, the pairs and share the common property (E.A), that is, there exist two sequences and in such that (3.7).
