A disjunctive programming problem corresponds to the minimization of an objective function on a constraint set which is a union of sets, for example, min f (x) s.t. min j∈ J g j (x) ≤ 0 where the functions f and g j are real valued defined on a Banach space X and J is a (possibly infinite) index set. This class of problems has been introduced by Balas [4] in 1974 and then studied by many author...

A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if X is a Banach space such that X ∗ has a SRBF, then X has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space X has an approximative Schauder frame, then X ∗ has a SRBF. Finally, the existence of a non-lin...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

There are traditionally many interactions between the convex geometry community and the Banach space community. In recent years, work is being done as well on problems that are related to notions and concepts from other fields. The interaction of convex geometry and Banach space theory, and also with other areas, is due to high dimensional phenomena which lie at the crossroad of convex geometry...

Environmental enrichment (EE) and voluntary exercise (VEx) have consistently been shown to increase adult hippocampal neurogenesis and improve spatial learning ability. Although it appears that these two manipulations are equivalent in this regard, evidence exists that EE and VEx affect different phases of the neurogenic process in distinct ways. We review the data suggesting that EE increases ...

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. This is used to prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a ...

We show that when a linear quotient map to a separable Banach space X has a Lipschitz right inverse, then it has a linear right inverse. If a separable space X embeds isometrically into a Banach space Y , then Y contains an isometric linear copy of X. This is false for every nonseparable weakly compactly generated Banach space X. Canonical examples of nonseparable Banach spaces which are Lipsch...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

The browser has become the de facto platform for everyday computation. Among the many potential attacks that target or exploit browsers, vulnerabilities in browser extensions have received relatively little attention. Currently, extensions are vetted by manual inspection, which does not scale well and is subject to human error. In this paper, we present VEX, a framework for highlighting potenti...