Search results for "Pointwise convergence"
showing 4 items of 4 documents
Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions
2016
[EN] We show a Dvoretzky-Rogers type theorem for the adapted version of the q-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector value…
VARIANTS OF A SELECTION PRINCIPLE FOR SEQUENCES OF REGULATED AND NON-REGULATED FUNCTIONS
2008
Let $T$ be a nonempty subset of $\RB$, $X$ a metric space with metric $d$ and $X^T$ the set of all functions mapping $T$ into $X$. Given $\vep>0$ and $f\in X^T$, we denote by $N(\vep,f,T)$ the least upper bound of those $n\in\NB$, for which there exist numbers $s_1,\dots,s_n,t_1,\dots,t_n$ from $T$ such that $s_1\vep$ for all $i=1,\dots,n$ ($N(\vep,f,T)=0$ if there are no such $n$'s). The following pointwise selection principle is proved: {\em If a sequence of functions\/ $\{f_j\}_{j=1}^\infty\subset X^T$ is such that the closure in $X$ of the sequence\/ $\{f_j(t)\}_{j=1}^\infty$ is compact for each $t\in T$ and\/ $\limsup_{j\to\infty}N(\vep,f_j,T)0$, then\/ $\{f_j\}_{j=1}^\infty$ contains …
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
A pointwise selection principle for metric semigroup valued functions
2008
Abstract Let ∅ ≠ T ⊂ R , ( X , d , + ) be an additive commutative semigroup with metric d satisfying d ( x + z , y + z ) = d ( x , y ) for all x , y , z ∈ X , and X T the set of all functions from T into X . If n ∈ N and f , g ∈ X T , we set ν ( n , f , g , T ) = sup ∑ i = 1 n d ( f ( t i ) + g ( s i ) , g ( t i ) + f ( s i ) ) , where the supremum is taken over all numbers s 1 , … , s n , t 1 , … , t n from T such that s 1 ⩽ t 1 ⩽ s 2 ⩽ t 2 ⩽ ⋯ ⩽ s n ⩽ t n . We prove the following pointwise selection theorem: If a sequence of functions { f j } j ∈ N ⊂ X T is such that the closure in X of the set { f j ( t ) } j ∈ N is compact for each t ∈ T , and lim n → ∞ ( 1 n lim N → ∞ sup j , k ⩾ N , j…