Sentence examples for be two positive functions from inspiring English sources

Let and be two positive functions defined on an interval, decreasing in,, (4.6).

Theorem 8 Let f and g be two positive functions on T t 0 and p ≠ 0 be a real number.

Theorem 5 Let f and g be two positive functions defined on T t 0 such that for all t > 0, m = min 0 ≤ τ ≤ t f g , M = max 0 ≤ τ ≤ t f g.

Theorem 9 Let p, f and g be three positive functions on T t 0 satisfying (19).

Corollary 4 Let p, f and g be three positive functions on T t 0 satisfying (20).

A look at the twisted basic estimate (14) shows that there are two positive functions we must choose, namely (tau ) and (A) (with (tau ) smooth).

For any fixed r ∈ [ 0, 1 ], assume f ̲ ( x ; r ) and f ¯ ( x ; r ) are Riemann-integrable on [ a, b ] for every b ≥ a, and assume there are two positive functions M ̲ ( r ) and M ¯ ( r ) such that ∫ a b | f ̲ ( x ; r ) | d x ≤ M ̲ ( r ) and ∫ a b | f ¯ ( x ; r ) | d x ≤ M ¯ ( r ) for every b ≥ a.

Let f and g be two positive integrable functions on interval ([a,infty)). Suppose that there exist four positive functions (varphi_{1}), (varphi _{2}), (psi_{1}), and (psi_{2}) satisfying the conditions (2.1).

Let f and g be two positive integrable functions on ([a,T]) which satisfy the condition (2.1) with the functions (varphi_{1}), (varphi_{2}), (psi_{1}), and (psi_{2}) in (3.1), (3.2), (3.3), and (3.4), respectively.

Let f and g be two positive integrable functions on ([a, infty)), (ageq0). Assume that there exist four positive integrable functions (varphi_{1}), (varphi_{2}), (psi_{1}), and (psi_{2}) satisfying ((H_{1})).

Let (h, k : mathbb{R} rightarrowmathbb{R}^) be two positive continuous functions.