Sentence examples for mappings are nonexpansive from inspiring English sources

We note that averaged mappings are nonexpansive.

In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive.

Furthermore, Dinh, Son, Jiao and Kim [16] proposed the linesearch algorithm which combines the extragradient method incorporated with the Armijo linesearch rule for solving the problem (FPSCSEP) in real Hilbert spaces under the assumptions that the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive.

Noticing that relatively nonexpansive mappings are nonexpansive in Hilbert spaces, then for any n ∈ N ∪ { 0 }, ∥ u n − p ∥ 2 = ∥ T r n y n − p ∥ 2 = ∥ T r n y n − T r n p ∥ 2 ≤ ∥ y n − p ∥ 2. From the proof of Step 2 in Theorem 3.1, we have ∥ u n − p ∥ 2 ≤ ∥ x n − p ∥ 2 + θ n.

We begin to observe that the mappings and are nonexpansive for all since they are compositions of nonexpansive mappings (see [22, page 419]).

In Hilbert spaces, every nonexpansive mappings are relatively nonexpansive, and is the identity operator.

Mappings of type Γ are nonexpansive; affine nonexpansive mappings are of type Γ; Mappings of type Γ have convex fixed point sets.

For order preserving mappings T, which are nonexpansive in L1 and L∞, two principal, mutually equivalent results are shown.

It is well known that nonexpansive mappings are 0-nonexpansive.

Since G and S A are nonexpansive mappings, we have B is a nonexpansive mapping.

Note that the class of κ-strictly pseudo-contractions strictly includes the class of nonexpansive mappings, that is, nonexpansive mapping is a 0-strictly pseudo-contraction mapping.