0000000001335290
AUTHOR
Caponetti, Diana
showing 4 related works from this author
On k-ball contractive retractions in F-normed ideal spaces
2010
Let X be an infinite dimensional F-normed space and r a positive number such that the closed ball B_r(X) of radius r is properly contained in X. For a bounded subset A of X, the Hausdorff measure of noncompactness gamma(A) of A is the infimum of all $\eps >0$ such that A has a finite $\eps$-net in X. A retraction R of B_r(X) onto its boundary is called k-ball contractive if $\gamma(RA) \le k \gamma(A)$ for each subset A of B_r(X). The main aim of this talk is to give examples of regular F-normed ideal spaces in which there is a 1-ball contractive retraction or, for any $\eps>0$, a $(1+ \eps)$-ball contractive retraction with positive lower Hausdorff measure of noncompactness.
MR2524371 (2010g:47114) Domínguez Benavides, T.; García Falset, J.; Llorens-Fuster, E.; Lorenzo Ramírez, P. Fixed point properties and proximinality …
2010
In the paper under review the authors mainly investigate the existence of a fixed point for nonexpansive mappings in the general setting of strictly $L(\tau)$ Banach spaces. They consider a linear topology $\tau$ on a Banach space $(X, \|\cdot \|)$, weaker than the norm topology, then the Banach space $X$ is a strictly $L(\tau)$ space if there exists a continuous function $\delta:[0, \infty[ \times [0, \infty[ \to [0, \infty[$ such that $\delta(\cdot,s)$ and $\delta(r, \cdot)$ are strictly increasing; $\delta(0,s)=s$, for every $s \in [0, \infty[$; and $\phi_{(x_n)}(y)= \delta (\phi_{(x_n)}(0), \|y\|)$, for every $y \in X$ and for every bounded and $\tau$-null sequence $(x_n)$, where $\phi_…
MR2410211 (2009b:47107) Păcurar, Mădălina Viscosity approximation of fixed points with $\phi$-contractions. Carpathian J. Math. 24 (2008), no. 1, 88-…
2009
Let T be a nonexpansive self-mapping of a closed bounded convex subset Y of a Hilbert space. For l in (0, 1), the author considers the iteration xl = lf(xl)+(1−l)Txl, where f from Y to Y is a $\phi$-contraction. Then, the author proves that (xl)l converges strongly as l goes to 0 to the unique fixed point of the $\phi$-contraction Pof, where P is the metric projection of Y onto the set FT of fixed points of T. The viscosity approximation method of the paper is obtained from the method proposed by A. Moudafi [J. Math. Anal. Appl. 241 (2000), no. 1, 46–55; MR1738332 (2000k:47085)] for mappings in Hilbert spaces, and by H. K. Xu [J. Math. Anal. Appl. 298 (2004), no. 1, 279–291; MR2086546 (2005…
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…