Sentence examples for e g for every from inspiring English sources

Indeed, the Krasnoselskii sequence ({x_{n}}) will satisfy ((x_{n},x_{n+1} in E(G)) for every n.

As a consequence, we have ((f^{n} x_{0}, x) in E(G)) for every (n geq1).

Condition (ii)′ in Corollary 3.7 can be replaced by: if ({x_{n}} subset S) is a sequence in (mathcal{T}_{N}(f,G,x_{0})) converging to some (x in S), then there exists a subsequence ({x_{n_{k}}}) of ({x_{n}}) such that ((x_{n_{k}},x) in E(G)) for every k large enough.

Note that if G is a reflexive transitive digraph defined on X, then property implies the following property: for any sequence ((x_{n})_{n geq1}) in X such that ((x_{n}, x_{n+1} in E(G)) for (n geq1) and ω is a weak-cluster point of ((x_{n})_{ngeq1}), we have ((x_{n}, omega in E(G)) for every (n geq1).

for any sequence ((x_{n})_{n inmathbb{N}}) in X such that ((x_{n}, x_{n+1} in E(G)) for (n inmathbb{N}) and ω is a weak-cluster point of ((x_{n})_{ninmathbb{N}}), then there exists a subsequence ((x_{phi(n)})_{ninmathbb{N}}) which converges weakly to ω and ((x_{phi(n)}, omega in E(G)) for every (n geq1).

Note that if G is a reflexive transitive digraph defined on X, then property implies the following property: For any ((x_{n})_{n geq1}) in X, if (x_{n}) ω-converges to x and ((x_{n}, x_{n+1} in E(G)) for (n geq1), then ((x_{n}, x in E(G)) for every (n geq1).

Koh, T. M. et al. Formamidinium tin-based perovskite with low E g for photovoltaic applications.

was detected (Fig. 3, panel D, F for Jj and panel C, E, G for jj).

Definition 1.2 If μ is a measure on then X has the Radon-Nikodym property with respect to μ if for every countably additive vector measure γ on with values in X which has bounded variation and is absolutely continuous with respect to μ, there is a Bochner integrable function g : Ω ⟶ X such that γ ( E ) = ∫ E g d μ. for every set E ∈ Σ.

We say that a mapping (f: Xto X) is a G-contraction if f preserves edges of G, i.e., for every (x,yin X), (x,y) in E(G) quad Rightarrowquad bigl(f(x),f y bigr) in E(G) and there exists (alpha in 0,1)) such that, for (x,yin X), (x,y) in E(G quad Rightarrowquad dbigl(f(x),f y bigr) lealpha d x,y).

We say that a mapping (T : Xto X) is a G-contraction if T preserves edges of G, i.e., for every (x,y in X), (x, y)in E(G quad Rightarrowquad(Tx,Ty) in E(G) (1.5) and there exists (alphain 0,1)) such that (x, y in X ), (x, y)in E G) quadRightarrowquad d(Tx,Ty leqalpha d x,y).