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The Davis–Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between certain population and sample eigenvalues. We present a variant of this result that depends only on a population(More)
Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping(More)
The laser ablation fast pulse discharge plasma spectroscopy (LA-FPDPS) technique has demonstrated its validity to enhance the optical emission of laser-induced plasma. It has the potential to improve the performance of traditional LIBS measurement. Very recently, LA-FPDPS with a nanosecond pulse discharge circuit has been developed, which has a better(More)
and Applied Analysis 3 Next we adopt the following notation: i xn → x means that xn converges strongly to x; ii xn ⇀ x means that xn converges weakly to x; iii ωw xn : {x : ∃xnj ⇀ x} is the weak ω-limit set of the sequence {xn}. Recall that a function f : H → R is called convex if f ( λx 1 − λ y ≤ λf x 1 − λ fy, 2.4 for all λ ∈ 0, 1 and ∀x, y ∈ H. It is(More)
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