Sentence examples for mappings with fixed from inspiring English sources

The class of quasi-nonexpansive mappings properly contains the class of nonexpansive mappings with fixed points; see, for example, [8].

It is easy to see that the class of pseudocontractive mappings with fixed points is a subclass of the class of hemicontractive mappings.

It is easy to see that the class of pseudocontractive mappings with fixed points is a subset of the class of hemicontractions.

It is easy to see that the class of pseudocontractive mappings with fixed points is a subclass of the class of hemicontractions.

From the above definitions, we note that the class of demicontractive operators contains important operators such as the directed operators, the quasi-nonexpansive operators and the strictly pseudocontractive mappings with fixed points.

From the above definitions, we note that the class of demicontractive mappings is fundamental; it includes many kinds of nonlinear mappings such as the directed mappings, the quasi-nonexpansive mappings, and the strictly pseudo-contractive mappings with fixed points as special cases.

Let f : C → C be a contraction with constant ρ > 0 and S, T : C → C be two nonexpansive mappings with Fix ( T ) ≠ ∅.

Corollary 3.2 Let f : C → H be a ρ-contraction with a coefficient ρ ∈ [ 0, 1 ) and S, T : C → C be two nonexpansive mappings with Fix ( T ) ≠ ∅.

Theorem 3.1LetCbe a nonempty, closed, and convex subset of a real Hilbert spaceHand let T : C → C be a uniformlyL-Lipschitzian and asymptotically quasi-nonexpansive mappings with Fix ( T ) ∩ Γ ≠ ∅ and { k n } ⊂ [ 1, ∞ ) for all n ∈ N such that ∑ n = 1 ∞ ( k n − 1 ) < ∞.

where are two nonexpansive mappings with the set of fixed points.

Let U : H 1 → H 1 and T : H 2 → H 2 be two L-Lipschitzian demicontractive mappings with nonempty Fix ( U ) = C and Fix ( T ) = Q.