Search results for "Measure of noncompactness"
showing 10 items of 14 documents
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.
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.
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 .
MR2502017 (2010c:46055) Angosto, C.; Cascales, B. Measures of weak noncompactness in Banach spaces. Topology Appl. 156 (2009), no. 7, 1412--1421. (Re…
2010
The authors consider for a bounded subset H of a Banach space E the De Blasi measure of weak noncompactness w(H) and the measure of weak noncompactness g(H) based on Grothendieck’s double limit criterion. They also deal with the quantitative characteristics k(H) and ck(H) which represent, respectively, the worst distance to E of the weak*-closure of H in the bidual of E and the worst distance to E of the sets of weak*-cluster points in the bidual of E of sequences in H. The authors prove the following chain of inequalities ck(H) < = k(H) < = g(H) < = 2ck(H) < = 2k(H) < = 2w(H), which, in particular, shows that ck, k and g are equivalent. The authors show that ck = k in the class of Banach s…
MR2543732 (2010g:46038) Colao, Vittorio; Trombetta, Alessandro; Trombetta, Giulio Hausdorff norms of retractions in Banach spaces of continuous funct…
2009
A retraction $R$ from the closed unit ball of a Banach space $X$ onto its boundary is called $k$-ball contractive if there is $k \ge 0$ such that $ \gamma_X(RA) \le k \gamma_X(A) $ for each subset $ A$ of the closed unit ball, where $\gamma_X$ denote the Hausdorff (ball) measure of noncompactness. In the paper under review the authors consider the problem of evaluating the Wo\'{s}ko constant, which is the infimum of all numbers $k$'s for which there is a $k$-ball contractive retraction from the closed unit ball onto the sphere, in Banach spaces of real continuous functions defined on domains which are not necessarily bounded or finite dimensional. The paper extends some previous results val…
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.
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.