Sentence examples for self contraction from inspiring English sources

Let be a complete metric space and let be a self contraction on, that is, there exists such that for all.

The self contraction mapping f : H → H in [[28], Theorem 3.2] is extended to the case of a nonself Lipschitzian mapping V : C → X on a nonempty, closed, and convex subset C of a real q-uniformly smooth Banach space X.

(2) The self contraction mapping f : H → H in [[28], Theorem 3.2] is extended to the case of a nonself Lipschitzian mapping V : C → X on a nonempty, closed, and convex subset C of a real q-uniformly smooth Banach space X.   (3) The control condition (C3) in [[28], Theorem 3.2] is removed by weaker than control condition | α n + 1 − α n | ≤ ∘ ( α n ) + σ n with ∑ n = 1 ∞ σ n < ∞.  .

Main result for self contractions on generalized metric spaces is Perov's fixed point theorem; see [1].

More precisely, for two given nonempty closed subsets A and B of a complete metric space ((X,d)), a non-self contraction (T : Ato B) does not necessarily have a fixed point.

where f : C → H is a fixed non-self contraction and { t n } is a sequence in ( 0, 1 ) satisfying the conditions: (S1) lim n → ∞ t n = 0 and ∑ n = 1 ∞ t n = ∞, (S2) either ∑ n = 1 ∞ | t n + 1 − t n | < ∞ or t n + 1 / t n → 0 as n → ∞.

A great deal of articles on the subject investigate the non-self-contraction mappings on metric spaces.

Figures 9 and  10 suggest that a too high formation temperature should prevent the self-contraction of SCCO2 for a maximum storage capacity in place.

The (self- contraction mapping (f:Hrightarrow H) in [13], Theorem 10 iself- contraction case of a Lipschitzian (possibly nonself-)mapping (U:Crightarrow H) on a nonempty, closed, and convex subset C of Hrightarrow

Such as the self-contraction mapping f : H → H in [15, 16, 19] is extended to the case of a Lipschitzian (possibly non-self- mapping U : C → H onon-self- mappinged conon-self- mappingH.

74 5844-5850, 2011) studied and established best proximity point theorems for proximal contractions of the first and the second kinds which are more general than the fixed point theorems of self-contractions.