MEASURES OF NONCOMPACTNESS IN ULTRAPRODUCTS
نویسندگان
چکیده
منابع مشابه
Inequivalent measures of noncompactness
Two homogeneous measures of noncompactness β and γ on an infinite dimensional Banach space X are called “equivalent” if there exist positive constants b and c such that bβ(S) ≤ γ (S) ≤ cβ(S) for all bounded sets S ⊂ X . If such constants do not exist, the measures of noncompactness are “inequivalent.”Weask a foundational questionwhich apparently has not previously been considered: For what infi...
متن کاملApplication of measures of noncompactness to infinite system of linear equations in sequence spaces
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کاملapplication of measures of noncompactness to infinite system of linear equations in sequence spaces
g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کاملConstruction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations
In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...
متن کاملInequivalent Measures of Noncompactness and the Radius of the Essential Spectrum
The Kuratowski measure of noncompactness α on an infinite dimensional Banach space (X, ‖ · ‖) assigns to each bounded set S in X a nonnegative real α(S) by the formula α(S) = inf{δ > 0 | S = n ⋃ i=1 Si for some Si with diam(Si) ≤ δ, for 1 ≤ i ≤ n <∞}. In general a map β which assigns to each bounded set S in X a nonnegative real and which shares most of the properties of α is called a homogeneo...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2009
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972709000197