Sentence examples for mappings including the from inspiring English sources

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).

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 ).

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.