Sentence examples for mappings include the from inspiring English sources

A mapping T of C into itself is called nonexpansive if ∥Tx - Ty∥ ≤ ∥x - y∥, for all x, y ∈ C. We denote by F T) the set of fixed points of T. Clearly, the class of pseudo-contractive mappings include the class of nonexpansive and strict pseudo-contractive mappings.

This interesting class of mappings includes the metric projections [11].

Obviously, the class of monotone mappings includes the class of the α-inverse strongly monotone mappings.

It is obvious that the class of quasi-pseudocontractive mappings includes the class of demicontractive mappings.

Hence, the class of averaged nonexpansive mappings includes the class of firmly nonexpansive mappings.

Clearly, the class of γ ¯ -strongly monotone mappings includes the class of strongly positive mappings.

Clearly, the class of monotone mappings includes the class of γ-inverse strongly monotone mappings.

Therefore, the class of -strictly pseudocontractive mappings includes the class of nonexpansive mappings.

Clearly, the class of pseudo-contractive mappings includes the class of strict pseudo-contractive mappings and non-expansive mappings.

It is clear that the class of strictly pseudocontractive mappings includes the class of nonexpansive mappings as a special case.

Note that the class of k-strictly pseudocontractive mappings includes the class of nonexpansive mappings as a subclass.