Sentence examples for if i a from inspiring English sources

We have that if i(A, K ∩ Ω, K) ≠0, then A has a fixed point in K ∩ Ω.

The condition I a(i) ≤ I b(i) holds if and only if the suffix of S starting at position i is a substring of T. The total number of the occurrences is calculated as I a(0) − I b(0) + 1 if I a(0)≤ I b(0), and 0, otherwise.

If (I(a)) is empty, then the conjecture holds.

One important fact is that if (i (A, KcapOmega, K neq 0), then A has a fixed point in (KcapOmega), see Theorem 2.3.2 in [20].

One important fact is that if i ( A, K ∩ Ω, K ) ≠ 0, then A has a fixed point in K ∩ Ω.

A linear operator A is the infinitesimal generator of a (C_{0} -semigroup ({T(t)}_{{t}geq0} -semigrouply if (i) A is closed and (overline{D(A)}=E).

Let ϒ = ( σ 1, σ 2, …, σ k ) be a k-tuple of mapping from Λ k into itself such that σ i ∈ Ω A, B if i ∈ A and σ i ∈ Ω A, B ′ if i ∈ B. Let F : X k → X be a mixed monotone mapping.

A mapping A is accretive if and only if (I - A) is pseudo-contractive.

A mapping f : E 1 → E 2 is said to have the local property if I ˜ A f ( x ) = I ˜ A f ( I ˜ A x ). for any A ∈ F and x ∈ E 1.

f is said to have the local property if I ˜ A f ( x ) = I ˜ A f ( I ˜ A x ) for all x ∈ E and A ∈ F. It is well known from [16] that f : E → L ¯ 0 ( F ) is L 0 ( F ) -convex iff f has the local property and epi ( f ) is L 0 ( F ) -convex.

(iii) If I = ( a, b ) ⊆ R and g is a monotone function on I, then by g ( a ) and g ( b ) we mean the limits lim x → a + g ( x ) and lim x → b − g ( x ), respectively.