Sentence examples for mappings includes the from inspiring English sources

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

This class of mappings includes the resolvent of a maximal monotone operator and Alber's generalized projection.

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

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

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

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

The general framework for A-maximal monotonicity (also referred to as the A-monotonicity framework in literature) generalizes the general theory of set-valued maximal monotone mappings, including the H-maximal monotonicity (also referred to as H-monotonicity).

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.

Then { x n } Δ-converges to a fixed point of T. Further, in a CAT ( 1 ) space, Kimura et al. [5] proved the Δ-convergence theorem for a family of nonexpansive mappings including the following scheme: x n + 1 = ( 1 − α n ) x n ⊕ α n ( ( 1 − β n ) S x n ⊕ β n T x n ).

The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings.

From (1.1), we know that if T is nonexpansive, then it is asymptotically nonexpansive with a constant sequence ({1}), but the converse may be not true in general, which can be seen from the example in [4] that is asymptotically nonexpansive but it is not nonexpansive, thus, the class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as a subclass.