Search results for "Compactness"

Eigenvectors of k–ψ-contractive wedge operators

AbstractWe present new boundary conditions under which the fixed point index of a strict-ψ-contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k–ψ-contractive wedge operators.

Proper $k$-ball-contractive mappings in $C_b^m[0, + infty)$

2021

In this paper we deal with the Banach space C-b(m)[0,+infinity] of all m-times continuously derivable, bounded with all derivatives up to the order m, real functions defined on [0, +infinity). We prove, for any epsilon > 0, the existence of a new proper k-ball-contractive retraction with k < 1+epsilon of the closed unit ball of the space onto its boundary, so that the Wosko constant W-gamma(C-b(m)[0,+infinity]) is equal to 1.

On some parameters related to weak noncompactness in L1(μ,E)

2009

A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU(A) of a bounded set A in the Bochner space L1(μ,E) and two parameters Π(A) and Λ1(A).

Recensione: MR3198633 Reviewed Olszowy, Leszek A family of measures of noncompactness in the space L1loc(R+) and its application to some nonlinear Vo…

2014

Recensione: MR3038069 Reviewed Banaś, Józef; Ben Amar, Afif Measures of noncompactness in locally convex spaces and fixed point theory for the sum of…

2013

A note on boundary conditions for nonlinear operators

2008

We investigate boundary conditions for strict-$\psi$-contractive and $\psi$-condensing operators. We derive results on the existence of eigenvectors with positive and negative eigenvalues and we obtain fixed point theorems for classes of noncompact opera\-tors.

Eigenvectors of k-psi-contractive wedge operators

2008

We present new boundary conditions under which the fixed point index of a strict-$\psi$-contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k-$\psi$-contractive wedge operators.

On some parameters related to weak noncompactness in L1(μ,E)

2009

A measure of weak noncompactness γU is defined in a Banach space X in terms of convex compactness. We obtain relationships between the measure γU(A) of a bounded set A in the Bochner space L1(μ,E) and two parameters Π(A) and Λ1(A) related, respectively, to uniform integrability and weak-tightness. The criterion for relative weak compactness in L1(μ,E) is recovered.

MR2376860 (2009e:28048) Khurana, Surjit Singh Weak compactness of vector measures on topological spaces. Publ. Math. Debrecen 72 (2008), no. 1-2, 69-…

2009

Weak compactness of vector measures on topological spaces.

Compactness in Groups of Group-Valued Mappings

2022

We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Fréchet–Šmulian and Ascoli–Arzelà compactness criteria found in the literature.