Clearly, a cone metric space in the sense of Huang and Zhang is a special case of tvs-cone metric spaces when (X, d) is tvs-cone metric space with respect to a normal cone P. Definition 1.3.
The concept of cone metric space is more general than that of metric space, because each metric space is a cone metric space, and a cone metric space in the sense of Huang and Zhang is a special case of tvs-cone metric spaces when ( X, d ) is a tvs-cone metric space with respect to a normal cone P. Definition 2.2 [2.2.
Let (X, ||·|| c ) be a cone normed space with respect to a normal cone P in the real Banach space E, and { T n } n ∈ N 0 be a sequence of self-maps of X with ∩ n F(T n ) ≠ ∅, T0 = I and d c (T n x, q) ≤ (1 + α n ) d c (x, q) for all n ∈ N 0, x ∈ X and q ∈ ∩ n F(T n ) where ∑ n ∈ N 0 α n < ∞.
Let (X, ||·|| c ) be a cone normed space with respect to a normal cone P in the real Banach space E, and { T n } n ∈ N 0 be a sequence of self-maps of X with T0 = I, ∩ n F(T n ) ≠ ∅, and ||T m x - T m -1x|| ≤ ||T m -1x- T m -2x|| for all ∈ X, m ≥ 2. Consider the iteration procedure xn+1= f(T n, x n ) = α n x n + (1 - α n )T n x n where S n = 1 n ( T 0 + T 1 + ⋯ + T n - 1 ) and α n ∈ [0, 1).
Let (X, ||·||c) be a cone normed space with respect to a normal cone P in the real Banach space E, and { T n } n ∈ N 0 be a sequence of self-maps of X with T0 = I, ∩ n F(T n ) ≠ ∅, and ||T m x - T m -1x|| ≤ ||T m -1x- T m -2x|| for all x ∈ X, m ≥ 2. Consider the iteration procedure x n +1 = S n x n where S n = 1 n ( T 0 + T 1 + ⋯ + T n - 1 ).
Let (X, ||·|| c ) be a cone normed space with respect to a normal cone P in the real Banach space E, and { T n } n ∈ N 0 be a sequence of self-maps of X with T0 = I, ∩ n F(T n ) ≠ ∅, and ||T m x - T m -1x || ≤ ||T m -1x - T m -2x|| for all x ∈ X, m ≥ 2. Consider the iteration procedure x n +1 = f (T n, x n ) = α n x n + (1 - α n )S n x n where S n = 1 n ( T 0 + T 1 + ⋯ + T n - 1 ) and α n ∈ [0, 1).
In 1983 L. G. Brown introduced a spectral distribution measure for non-normal elements in a finite von Neumann algebra M with respect to a fixed normal faithful tracial state τ.
Let M be aσ-finite von Neumann algebra and let A be a maximal subdiagonal algebra of M with respect to a faithful normal conditional expectationΦ.
To quantify a selective response of a cancer cell line with respect to a control normal cell line, we define the selectivity S of a single drug or drug combination as S = v N v C where v N indicates the viability of normal cells (IMR90) after treatment, and v C the viability of cancer cells (A549) after treatment.
We construct a Toeplitz projection for every regular A-isometry T∈B(H n on a complex Hilbert space H and use it to determine the essential commutant of the set of all analytic Toeplitz operators formed with respect to an essentially normal regular A-isometry.
Conventional methods consider the events with low-probability with respect to a model of normal behavior as anomaly.
