Sentence examples for mappings do not from inspiring English sources

Hemi-relatively nonexpansive mappings do not require (F(T =widetilde{F}(T)).

However, some mappings do not have the commutative property as in the above example.

Quasi-ϕ-nonexpansive mappings and asymptotically quasi-ϕ-nonexpansive mappings do not require the restriction F ( T ) = F ˜ ( T ).

Quasi-ϕ-nonexpansive mappings and asymptotically quasi-ϕ-nonexpansive mappings do not require F ( T ) = F ˜ ( T ).

Moreover, we show that the existence of common fixed points for Mizoguchi-Takahashi's type multi-valued mappings do not require the condition of T-weakly commuting mappings.

The main difficulty encountered in this setting has to do with the fact that the mappings do not have a good behavior on the entire sets.

It is also interesting to note that this family of mappings does not belong to the class discussed in [23].

The class of -inverse strongly monotone mappings does not contain some important classes of mappings even in a finite-dimensional case.

We note that the concept of G-contraction for multi-valued mappings does not concern the concept of graph-preserving as seen for single-valued mappings.

The significant benefits of semitone mappings does not exist in CI users with MCI test, and this may be due to requirement of a long-term familiarization or more CI subjects.

(In contrast, it has been noted that the proof of the first author's fundamental fixed point theorem for nonexpansive mappings does not require the triangle inequality; see [3].) In the absence of relevant examples, it is not clear whether Branciari's concept of weakening the triangle inequality will prove useful in analysis.