Search results for "Compactness"

On the existence of at least a solution for functional integral equations via measure of noncompactness

2017

In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation ¶ \[u(t)=g(t,u(t))+\int_{0}^{t}G(t,s,u(s))\,ds,\quad t\in{[0,+\infty[},\] in the space of all bounded and continuous real functions on $\mathbb{R}_{+}$ , under suitable assumptions on $g$ and $G$ . Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.

A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

2019

We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.

A Mountain Pass Theorem for a Suitable Class of Functions

2009

Recensione: MR2928500 Cascales, Bernardo; Kalenda, Ondřej F. K.; Spurný, Jiří A quantitative version of James's compactness theorem. Proc. Edinb. Mat…

2013

Paper review

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.

Multiple positive solutions for singularly perturbed elliptic problems in exterior domains

2003

Abstract The equation − e 2 Δ u + a e ( x ) u = u p −1 with boundary Dirichlet zero data is considered in an exterior domain Ω = R N ⧹ ω ( ω bounded and N ⩾2). Under the assumption that a e ⩾ a 0 >0 concentrates round a point of Ω as e →0, that p >2 and p N /( N −2) when N ⩾3, the existence of at least three positive distinct solutions is proved.

Convergence-theoretic characterizations of compactness

2002

AbstractFundamental variants of compactness are characterized in terms of concretely reflective convergence subcategories: topologies, pretopologies, paratopologies, hypotopologies and pseudotopologies. Hyperquotient maps (perfect, quasi-perfect, adherent and closed) and quotient maps (quotient, hereditarily quotient, countably biquotient, biquotient, and almost open) are characterized in terms of various degrees of compactness of their fiber relations, and of sundry relaxations of inverse continuity.

Examples of proper k-ball contractive retractions in F-normed spaces

2007

Abstract Assume X is an infinite dimensional F -normed space and let r be a positive number such that the closed ball B r ( X ) of radius r is properly contained in X . The main aim of this paper is to give examples of regular F -normed ideal spaces in which there is a 1-ball or a ( 1 + e ) -ball contractive retraction of B r ( X ) onto its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X .

Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

2012

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

Completeness number of families of subsets of convergence spaces

2016

International audience; Compactoid and compact families generalize both convergent filters and compact sets. This concept turned out to be useful in various quests, like Scott topologies, triquotient maps and extensions of the Choquet active boundary theorem.The completeness number of a family in a convergence space is the least cardinality of collections of covers for which the family becomes complete. 0-completeness amounts to compactness, finite completeness to relative local compactness and countable completeness to Čech completeness. Countably conditional countable completeness amounts to pseudocompleteness of Oxtoby. Conversely, each completeness class of families can be represented a…