Search results for "measure of noncompactne"
showing 10 items of 16 documents
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.
Optimal retraction problem for proper $k$-ball-contractive mappings in $C^m [0,1]$
2019
In this paper for any $\varepsilon >0$ we construct a new proper $k$-ball-contractive retraction of the closed unit ball of the Banach space $C^m [0,1]$ onto its boundary with $k < 1+ \varepsilon$, so that the Wośko constant $W_\gamma (C^m [0,1])$ is equal to $1$.
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.
Recensione: MR3198633 Reviewed Olszowy, Leszek A family of measures of noncompactness in the space L1loc(R+) and its application to some nonlinear Vo…
2014
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.
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 Boundary Conditions for Wedge Operators on Radial Sets
2008
We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.
The class of F-contraction mappings with a measure of noncompactness
2017
In this chapter we review a class of contraction conditions, which are largely used to obtain interesting generalizations of the Banach fixed-point theorem in various abstract settings. We also present a new fixed-point existence result obtained by considering such a kind of contraction condition and a measure of noncompactness. Moreover, we show the applicability of these results in the theory of functional equations.