Sentence examples for a weak contraction from inspiring English sources

A self-mapping f on X is a weak contraction if the following contractive condition holds: d ( f x, f y ) ≤ d ( x, y ) − φ ( d ( x, y ) ), for all x, y ∈ X, where φ is an altering distance function.

A self-mapping f on X is called a weak contraction if the following contractive condition is satisfied: d ( f x, f y ) ≤ d ( x, y ) − φ ( d ( x, y ) ), for all x, y ∈ X, where φ is an altering distance function.

(2) Any mapping T satisfying the contractive condition (1.3) is a weak contraction.

Any mapping T satisfying the contractive condition (1.3) is a weak contraction.

Any Kannan mapping is a weak contraction.

Let be a weak contraction with a function.

Suppose that a non-decreasing self-mapping T : X → X is a weak-contraction mapping, that is, Ω ( T x, T 2 x, T y ) ≤ Ω ( x, T x, y ) − ϕ ( Ω ( x, T x, y ) ) for all  x, y ∈ X,  with  x ≤ T x, where ϕ ∈ Φ. Suppose also that inf { Ω ( x, y, x ) + Ω ( x, y, T x ) + Ω ( x, T x, y ) : x ≤ T x } > 0 for every y ∈ X with y ≠ T y.

A self-mapping T : X → X is said to be a weak-contraction mapping if itsatisfies the following condition: Ω ( T x, T 2 x, T y ) ≤ Ω ( x, T x, y ) − ϕ ( Ω ( x, T x, y ) ) for all  x, y ∈ X,  with  x ≤ y, where ϕ ∈ Φ. Corollary 12Let ( X, G, ≤ ) be a partially ordered completeG-metric space, and let Ω be anΩ-distance onX.

Berinde [18] introduced the notion of a -weak contraction and proved that a lot of the well-known contractive conditions do imply the -weak contraction.

Hence is a -weak contraction on and.

Then f is said to be a -weak contraction mapping.