Sentence examples for is a fixed element of from inspiring English sources

If a is a fixed element of the function space D∞, then x = (a, x) holds when x is the fixed point of a.

Let (f_{1}) and (g_{1}) be defined by (f_{1}|_{Lambda_{alpha }}=f alpha beta)) for every (alphainGamma) and (g_{1}|_{Lambda_{alpha }}=g alphabeta)) for every (alphainGamma), where β is a fixed element of Λ.

Let (f_{1}) and (g_{1}) be defined by (f_{1}|_{Lambda_{alpha }}=f alpha beta)) for every (alphainLambda_{m}) and (g_{1}|_{Lambda _{alpha }}=g alphabeta)) for every (alphainLambda_{m}), where β is a fixed element of Λ.

Let be a fixed element of.

Theorem 3.10 Let ( X, d X ) and ( R, d R ) be asymmetric metric spaces, such that d X and d R are real-valued distance functions, y ¯ be a fixed element of R, ℱ be any free filter of ℕ and suppose that (3.10.1) each subset of R, ℱ-closed and ℱ-forward bounded with respect to y ¯, is ℱ-compact.

The Halpern iterative process generates a sequence { x n } in the following manner: x 1 ∈ C, x n + 1 = α n u + ( 1 − α n ) T x n, ∀ n ≥ 1, where x 1 is an initial and u is a fixed element in C. Strong convergence of Halpern iterative process does not depend on metric projections.

We note that the Halpern approximation method [2], x_{n+1}=alpha_{n} u+ 1-alpha_{n}) t(x_{n}),qu+ 1-alpha_{n}N}, where u is a fixed element in E, is a special case of the Moudafi one.

where is a fixed element.

where u ∈ C is a fixed element.

By the linearity of F : X → R, F ′ ∈ X ∗ is a fixed element.

n ≥ 0, where u ∈ C is a fixed element.