Sentence examples for be an initial point from inspiring English sources
Initialization: Let (epsilon >0) be given, (mathbf {p}^{(0)}in C) be an initial point, set (r:=0;).
Let (x_{0}in X_{0}) be an initial point and suppose that the method (GPTM) reaches Step ((k)).
where T n = T n ( mod N ) (here the modN function takes values in I), { α n } be a real sequence in [ 0, 1 ], x 0 be an initial point in K. Sun [2] have extended this iterative process defined by Xu and Ori to a new iterative process for a finite family of asymptotically nonexpansive mappings, which is defined as follows: x n = α n x n − 1 + ( 1 − α n ) T i k x n, n ≥ 1, (2).
The number of patients was not the ideal to try to show the prevalence in the entire country, but it would be an initial point for future studies.
These risks of malignancy in patients without a tumor might be an initial point of consideration and give some guidance when planning to treat a patient with (a history of) a malignant disease.
A point with is an initial point, while a point with is a noninitial point.
The fact that ({x^{(0)}}) is an initial point of ({T^{(N }}) follows from Lemma 4.5 and Theorem 2.6.
where T λ n + 1 x n = T x n − λ n + 1 μ F ( T x n ) for all x n ∈ H, x 0 ∈ H is an initial point, F : H → H is an η-strongly monotone and k-Lipschitzian mapping, μ is a positive fixed constant.
In fact, let (Pi = mathbb{T}), (e_{Pi^=t_{0}), (delta (s,t)=delta_ s,t)) and (delta (s^{-1},t)=delta^{-1}(s,t)=delta_ s,t)), where (sin [t_{0},+infty)_{mathbb{T}^) and (t_{0}) is an initial point, then all the results from [15] become a particular case of the established results in this paper.
where { α n }, { β n }, { γ n }, { δ n } are four real sequences in [ 0, 1 ] satisfying α n + γ n ≤ 1 and β n + δ n ≤ 1 for all n ≥ 1, { u n }, { v n } are two sequences in K and x 0 is an initial point.
According to Theorem 2.6 to prove that ({x^{(0)}}) is an initial point of ({T^{(N }}) it is sufficient to prove that x in D_{N} quad text{and} quad E x) in J quad Rightarrowquad T^{(N)}(x) in D_{N}.
