The set-valued mapping T is called a fuzzy α-ψ-contractive mapping if the following implication takes place: x, y ∈ X, t > 0, α ( x, y, t ) ≤ η ( x, y, t ) ⇒ H M ( T x, T y, t ) ≥ ψ ( N ( x, y, t ) ), (1).
The set-valued mapping T is called a fuzzy ψ-p-contractive mapping if the following implication takes place: for any x 1, x 2 ∈ X and y 1 ∈ T x 1, there exists y 2 ∈ T x 2 such that P ( x 1, x 2, t ) > 0 ⇒ P ( y 1, y 2, t ) ≥ ψ ( P ( x 1, x 2, t ) ) for each t > 0. In particular, the fuzzy ψ-M-contraction corresponds to the fuzzy ψ-contraction according to [[7], Definition 3.1].
In particular, Mihet [2] introduced the concepts of fuzzy ψ-contractive mappings which enlarge the class of fuzzy contractions in [1], that is, the following implication takes place for the single-valued mapping T: M ( x, y, t ) > 0 ⇒ M ( T x, T y, t ) ≥ ψ ( M ( x, y, t ) ). for any x, y ∈ X and t > 0, where ψ is a function whose definition is given in Section 3.
The beauty of cinematic images is the work of the eye and also of the "I": it's the mark of the filmmaker's moral implication in what takes place onscreen.
He argues that Labour has essentially got things right, but that the attack on liberty, which he concedes by implication has taken place, was the result of excessive zeal.
Determining exactly when spawning takes place has important implications for reef management and clear economic benefits.
Such a shift, if it takes place, would have severe implications for hopes of a consensual peace between Israelis and Palestinians, and for wider regional stability.
The implication is that a considerable amount of sexual abuse takes place in the vicinity of the home, and sometimes within the home itself.
"This has really important implications," she says: It suggests that the harm that takes place in a family setting may reversible, too.
And the seemingly inevitable shift of Piazza to first base -- whether it takes place in 2003 or 2004 -- will have implications on what the team does this winter.
