Sentence examples for many nonexpansive mappings from inspiring English sources

The THVI (1.9) involves the HFPP for the nonexpansive mapping S and infinitely many nonexpansive mappings { T n } n = 1 ∞ but the problem in [[23], Theorem 21] involves no HFPP for nonexpansive mappings.  .

(iv) Our Theorems 3.1 and 3.2 extend Theorems 3.12 and 3.13 of [29] from one nonexpansive mapping T to infinitely many nonexpansive mappings ({T_{n}}^{infty}_{n=1}) and from one variational inequality to finitely many variational inequalities.

Moreover, these also extend Theorems 3.12 and 3.13 of [30] from one nonexpansive mapping T to infinitely many nonexpansive mappings ({T_{n}}^{infty}_{n=1}) and generalize Theorems 3.12 and 3.13 of [30] to the setting of finitely many variational inequalities.  .

In fact, there are many nonexpansive mappings which do not satisfy (1.8).

Then, as the composition of finitely many nonexpansive mappings, U is nonexpansive.

In this section, we prove the strong convergence theorem for infinitely many nonexpansive mappings in a real Hilbert space.

The first application is concerned with the image recovery problem which is equivalent to finding a common fixed point of finitely many nonexpansive self mappings.

The composition of finitely many strongly nonexpansive mappings is also strongly nonexpansive.

(ii) The composition of finitely many strongly nonexpansive mappings is also strongly nonexpansive.  .

Saejung also studied Halpern iterations with finitely and countably many different nonexpansive mappings sharing a fixed point.

In this note, we show that if finitely many firmly nonexpansive mappings defined on a real Hilbert space are given and each of these mappings is asymptotically regular, which is equivalent to saying that they have or "almost have" fixed points, then the same is true for their composition.