Sentence examples for a continuous and strict from inspiring English sources

be given where is a continuous and strict increasing function for all with.

For (fin C^{0}_{uparrow}(0,infty)), we have seen that (m_{f}) is a continuous and strict monotone mean.

Let the recursive inequality λ n + 1 ≤ λ n - α n ψ ( λ n ) + β n, n = 0, 1, 2 ⋯, be given, where ψ is a continuous and strict increasing function for all λ ≥ 0 with ψ(0) = 0. Then {λ n } converges to zero, as n → ∞.

Let { a n } and { b n } be two nonnegative real number sequences and { α n } a positive real number sequence satisfying the conditions: ∑ n = 1 ∞ α n = ∞ and lim n → ∞ b n α n = 0. Let the recursive inequality a n + 1 ≤ a n − α n φ ( a n ) + b n, n ≥ 0, where φ ( a ) is a continuous and strict increasing function for all a ≥ 0 with φ ( 0 ) = 0. Then lim n → ∞ a n = 0. Lemma 2.6 ([6]).

(A:Xrightarrow X^) is a continuous, bounded and strict monotone operator.

We write (A:Xrightarrow X^) bigllangle A u),vbigrrangle =int_{Omega}omega(x)|nabla u|^{p(x -2}nabla u nabla v,mathrm{d}x -2}nablaall u, vinabla(i) (A:Xrightarrow X^) is a continuous, bounded and strict monotone operator.

(3) is continuous and strict decreasing on with.

In, let be two nonempty compact and convex subsets, be continuous and strict monotone in.

However, even though efficient such continuous and strict treatments may not correspond to the needs and preferences of a majority of people.

Let H be a real Hilbert space, C a nonempty, closed, and convex subset of H, and S : C → C a uniformly continuous and asymptotically strict pseudocontraction in the intermediate sense.

In SVI, let be two compact and convex subset, and let and be two continuous mappings and strict monotone in and, respectively.