We say that a mapping f : X → X is an almost generalized s -contractive mapping if there exist L ≥ 0 and two altering distance functions ψ and φ such that ψ ( s d ( f x, f y ) ) ≤ ψ ( M s ( x, y ) ) − φ ( M s ( x, y ) ) + L ψ ( N ( x, y ) ) (2.1).
We say that a mapping f : X → X is an almost generalized s, a -contractive mapping if there exist L ≥ 0 and two altering distance functions ψ and φ such that ψ ( s d ( f x, f y, a ) ) ≤ ψ ( M a ( x, y ) ) − φ ( M a ( x, y ) ) + L ψ ( N a ( x, y ) ) (3.24).
Suppose that the following conditions hold: (i) T ( A i ) ⊆ A i + 1 for all i ∈ { 1, …, N } with A N + 1 : = A 1 ; (ii) there exist two altering distance functions ψ and φ such that ψ ( d ( T x, T y ) ) ≤ ψ ( d ( x, y ) ) − φ ( d ( x, y ) ) for all ( x, y ) ∈ A i × A i + 1 for all i ∈ { 1, …, N }. .
We say that a mapping f : X → X is a generalized s -weakly contractive mapping if there exist two altering distance functions ψ and φ such that ψ ( s p b ( f x, f y ) ) ≤ ψ ( M s f ( x, y ) ) − φ ( M s f ( x, y ) ) (3.1).
X = A ∪ B is a cyclic representation of X w.r.t. the pair ( f, g ) ; that is, f A ⊆ B and g B ⊆ A ; there exist two altering distance functions ψ, φ and a constant L ≥ 0, such that for arbitrary comparable elements x, y ∈ X with x ∈ A and y ∈ B, we have ψ ( s 2 p b ( f x, g y ) ) ≤ ψ ( M s ( x, y ) ) − φ ( M s ( x, y ) ) + L ψ ( N ( x, y ) ), (3.1).
X = A ∪ B is a cyclic representation of X w.r.t. the pair ( f, g ) ; that is, f A ⊆ B and g B ⊆ A ; there exist two altering distance functions ψ, φ and a constant L ≥ 0, such that for arbitrary comparable elements x, y ∈ X with x ∈ A and y ∈ B, we have ψ ( s 2 d ( f x, g y ) ) ≤ ψ ( M s ( x, y ) ) − φ ( M s ( x, y ) ) + L ψ ( N ( x, y ) ), (2.1).
She suggests, in fact, that nostalgia has two alter egos.
DSC investigations indicated that the threading prevents the crystallization of the crown ether and allows phase mixing to some extent, since two altered Tg's were observed.
The district found six altered transcripts for current seniors.
The translation in French of the three altered articles was then written in, in its proper place.
A job done slowly and right is better than one altered or abandoned.
