Sentence examples for mappings defined by from inspiring English sources

Throughout this paper, for a given mapping, let be the mappings defined by.

Let be mappings defined by (2.25).

Let be a sequence of mappings defined by (2.38).

Let be the bi-Jensen mappings defined by (2.11).

for some ; and associated composed mappings defined by ;, subject to.

We consider the set-valued mappings defined by (319).

Then a mappings define by is always asymptotically regular, that is, for every,.

Let f and g be two self-mappings defined by (fx=x^{3}), (gx=2-x).

We have the following crucial lemmas concerning the W-mappings defined by (1.17).

Let f and g be two self-mappings defined by fx=left { textstylebegin{array}{l@{quad}l} x, & mbox{if }0leq x< 2, 2,& mbox{if } x=2, 4,& mbox{if }2< x< +infty, end{array}displaystyle right.qquad gx=left { textstylebegin{array}{l@{quad}l} 4-x,& mbox{if }0leq x< 2, 2,& mbox{if } x=2, 7,& mbox{if }2< x< +infty.

If the switching law σ : Z 0 + → q ¯ ⊆ Z + is such that ρ k ≤ ρ / ( ∑ i = 0 μ M 0 i ), ∀ k ∈ Z 0 +, for some given real constant ρ ∈ ( 0, 1 ) then all the sequence of composite self-mappings defined by T ˆ ( n k, n k + 1 ) = T σ ( n k + 1 − 1 ) ⋯ T ˆ σ ( n k ) on X are strict contractions of contractive constant ρ.