Sentence examples for be an unbounded function from inspiring English sources

Lemma 2.2 Let f : G → K be an unbounded function satisfying (2.2).

Let f be an unbounded function such that there is a positive constant c such that (f ( xy ) geq cf ( x ) f ( y ) ) for all (xgeq 0), (ygeq 0) [42].

Let g be a unbounded function and ϕ ( x + i, y ) ≤ ϕ ( x, y ) Open image in new window.

Then f(x +y) = g y)f(x) for allx,y ∈ S. Let g be a unbounded function and I = {i ∈S ∥ |g(i)| > 1}, then sets ρ i (x) := x + i, c i := g(i) and ψ i := ϕ x,i) for all x ∈S and any i ∈ I. Since ρ i ρ j = ρ i ρ j and ψ i (ρ i (x)) ≤ ψ i (x) for all x ∈ S and any i∈ I, so by Corollary (3.2), there is an unique functionT such that T ( ρ i ( x ) ) = c i T ( x ) Open image in new window.

Lemma 2.3 Assume that g is bijective and f : G → K is an unbounded function satisfying the inequality (2.2).

for all x, y ∈ G. Lemma 2.1 Assume that g = σ is an involution and f : G → K is an unbounded function satisfying the inequality (2.2).

Lemma 2.4 Assume that g = σ is an involution and f : G → K is an unbounded function satisfying the inequality (2.3).

It is obvious that (f t, x in C^{0,1}(mathbf{S}^{1}times mathbb{R})) is an unbounded function satisfying conditions ((A_{1})) and ((A_{2})) in Theorem 1.1 if (d=e^{2}) and (mu =1).

Since g is a unbounded function,from last inequality T = f, which implies that f ( ρ i ( x ) ) = c i f ( x ) Open image in new window.

Let f be an unbounded modulus function.

Let f be an unbounded modulus function and α be any real number such that (0< alphaleq1).